{ "cells": [ { "cell_type": "code", "execution_count": 2, "id": "2b4123b8", "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "code", "execution_count": 3, "id": "13f9d8a2", "metadata": {}, "outputs": [], "source": [ "f=sin(sin(sin(exp(x^2))))" ] }, { "cell_type": "code", "execution_count": 4, "id": "2a3461d5", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\sin\\left(\\sin\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)\\right)\\)" ], "text/latex": [ "$\\displaystyle \\sin\\left(\\sin\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)\\right)$" ], "text/plain": [ "sin(sin(sin(e^(x^2))))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "4539156e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle 2 \\, x \\cos\\left(e^{\\left(x^{2}\\right)}\\right) \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right) \\cos\\left(\\sin\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)\\right) e^{\\left(x^{2}\\right)}\\)" ], "text/latex": [ "$\\displaystyle 2 \\, x \\cos\\left(e^{\\left(x^{2}\\right)}\\right) \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right) \\cos\\left(\\sin\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)\\right) e^{\\left(x^{2}\\right)}$" ], "text/plain": [ "2*x*cos(e^(x^2))*cos(sin(e^(x^2)))*cos(sin(sin(e^(x^2))))*e^(x^2)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d=derivative(f,x)\n", "d.simplify_full()" ] }, { "cell_type": "code", "execution_count": 9, "id": "20295339", "metadata": {}, "outputs": [], "source": [ "D=derivative(f,x,8)" ] }, { "cell_type": "code", "execution_count": 10, "id": "529cbff8", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle 16 \\, {\\left(224 \\, {\\left(2 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} e^{\\left(8 \\, x^{2}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right) - 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42 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right) e^{\\left(7 \\, x^{2}\\right)}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{4} + 2520 \\, {\\left(28 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 3 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{2} - {\\left(21488 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{8} e^{\\left(8 \\, x^{2}\\right)} - 10752 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} + 784 \\, {\\left(76 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} - 49 \\, {\\left(4848 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 520 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} + {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4} + {\\left(162608 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 15904 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} - 49 \\, {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)} + {\\left(2032 \\, x^{8} + 14112 \\, x^{6} + 26040 \\, x^{4} + 12600 \\, x^{2} + 735\\right)} e^{\\left(2 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{2} - 840 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} + 21 \\, {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)} + 14 \\, {\\left(4704 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} e^{\\left(7 \\, x^{2}\\right)} - 1400 \\, {\\left(28 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{3} + 3 \\, {\\left(3584 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} + 100 \\, {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)} - {\\left(1104 \\, x^{8} + 4816 \\, x^{6} + 5400 \\, x^{4} + 1500 \\, x^{2} + 45\\right)} e^{\\left(3 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{2} - 1680 \\, {\\left(42 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} e^{\\left(7 \\, x^{2}\\right)} + 5 \\, {\\left(28 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{3} - 42 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right) e^{\\left(7 \\, x^{2}\\right)}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right) - 14 \\, {\\left(336 \\, {\\left(2 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} e^{\\left(8 \\, x^{2}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right) - {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{7} e^{\\left(7 \\, x^{2}\\right)}\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{5} - 200 \\, {\\left(28 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{7} e^{\\left(7 \\, x^{2}\\right)} + {\\left(112 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} - 84 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{3} e^{\\left(7 \\, x^{2}\\right)} - {\\left(56 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} e^{\\left(8 \\, x^{2}\\right)} - 24 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{2} e^{\\left(8 \\, x^{2}\\right)} + 3 \\, {\\left(20 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{3} + 3 \\, {\\left(224 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{7} e^{\\left(7 \\, x^{2}\\right)} - 100 \\, {\\left(112 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} + {\\left(3584 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} + 500 \\, {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)} - {\\left(1104 \\, x^{8} + 4816 \\, x^{6} + 5400 \\, x^{4} + 1500 \\, x^{2} + 45\\right)} e^{\\left(3 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{3} + 60 \\, {\\left(56 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - 5 \\, {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right) - {\\left(448 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} e^{\\left(8 \\, x^{2}\\right)} + 240 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 300 \\, {\\left(20 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4} + 3 \\, {\\left(432 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} + 120 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} - {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{2} - 60 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)\\right)} \\sin\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)\\right)} \\sin\\left(\\sin\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)\\right)\\)" ], "text/latex": [ "$\\displaystyle 16 \\, {\\left(224 \\, {\\left(2 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} e^{\\left(8 \\, x^{2}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right) - {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{7} e^{\\left(7 \\, x^{2}\\right)}\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{7} - 280 \\, {\\left(112 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{7} e^{\\left(7 \\, x^{2}\\right)} + {\\left(112 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} - 84 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{3} e^{\\left(7 \\, x^{2}\\right)} - {\\left(224 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} e^{\\left(8 \\, x^{2}\\right)} - 24 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{2} e^{\\left(8 \\, x^{2}\\right)} + 3 \\, {\\left(20 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{5} - 14 \\, {\\left(3136 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{7} e^{\\left(7 \\, x^{2}\\right)} + 500 \\, {\\left(112 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} - {\\left(37184 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} + 500 \\, {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)} - {\\left(1104 \\, x^{8} + 4816 \\, x^{6} + 5400 \\, x^{4} + 1500 \\, x^{2} + 45\\right)} e^{\\left(3 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{3} - 60 \\, {\\left(56 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - 5 \\, {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right) - {\\left(6272 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} e^{\\left(8 \\, x^{2}\\right)} - 240 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} + 1500 \\, {\\left(20 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4} - 3 \\, {\\left(3632 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} + 120 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} - {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{2} + 60 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{3} + {\\left(46816 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{7} e^{\\left(7 \\, x^{2}\\right)} + 3920 \\, {\\left(112 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} - 14 \\, {\\left(28336 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - 500 \\, {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)} + {\\left(1104 \\, x^{8} + 4816 \\, x^{6} + 5400 \\, x^{4} + 1500 \\, x^{2} + 45\\right)} e^{\\left(3 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{3} + {\\left(46816 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - 3920 \\, {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)} - 14 \\, {\\left(1104 \\, x^{8} + 4816 \\, x^{6} + 5400 \\, x^{4} + 1500 \\, x^{2} + 45\\right)} e^{\\left(3 \\, x^{2}\\right)} + {\\left(16 \\, x^{8} + 224 \\, x^{6} + 840 \\, x^{4} + 840 \\, x^{2} + 105\\right)} e^{\\left(x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right) - {\\left(93632 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} e^{\\left(8 \\, x^{2}\\right)} + 3344 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} + 11760 \\, {\\left(20 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4} - 42 \\, {\\left(2608 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 120 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} + {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{2} - 784 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} - 7 \\, {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)} + {\\left(2032 \\, x^{8} + 14112 \\, x^{6} + 26040 \\, x^{4} + 12600 \\, x^{2} + 735\\right)} e^{\\left(2 \\, x^{2}\\right)}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right) + {\\left(448 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{8} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{6} e^{\\left(8 \\, x^{2}\\right)} - 3344 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{8} e^{\\left(8 \\, x^{2}\\right)} + 672 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 784 \\, {\\left(76 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} + 7 \\, {\\left(10608 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 520 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} + {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4} + 840 \\, {\\left(20 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{8} e^{\\left(8 \\, x^{2}\\right)} - 60 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4} e^{\\left(8 \\, x^{2}\\right)} + 84 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} e^{\\left(7 \\, x^{2}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right) + {\\left(76 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6}\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{4} - {\\left(21488 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 784 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} - 49 \\, {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)} + {\\left(2032 \\, x^{8} + 14112 \\, x^{6} + 26040 \\, x^{4} + 12600 \\, x^{2} + 735\\right)} e^{\\left(2 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{2} + 42 \\, {\\left(208 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{8} e^{\\left(8 \\, x^{2}\\right)} + 240 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} + 120 \\, {\\left(76 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} - {\\left(3312 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} + 520 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} - {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4} - 120 \\, {\\left(28 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 3 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{2} + 80 \\, {\\left(126 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} e^{\\left(7 \\, x^{2}\\right)} + 5 \\, {\\left(28 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{3} - 42 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right) e^{\\left(7 \\, x^{2}\\right)}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{2} + 840 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} - 21 \\, {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)} - 14 \\, {\\left(4704 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} e^{\\left(7 \\, x^{2}\\right)} - 200 \\, {\\left(28 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{3} + 3 \\, {\\left(224 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} + 100 \\, {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)} - {\\left(1104 \\, x^{8} + 4816 \\, x^{6} + 5400 \\, x^{4} + 1500 \\, x^{2} + 45\\right)} e^{\\left(3 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\sin\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)\\right)} \\cos\\left(\\sin\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)\\right) + 16 \\, {\\left(16 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{8} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{8} e^{\\left(8 \\, x^{2}\\right)} + 672 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{8} e^{\\left(8 \\, x^{2}\\right)} - 5040 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 840 \\, {\\left(76 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} + 56 \\, {\\left(76 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{8} e^{\\left(8 \\, x^{2}\\right)} - 60 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4} e^{\\left(8 \\, x^{2}\\right)} + 84 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} e^{\\left(7 \\, x^{2}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right) + {\\left(76 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6}\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{6} - 21 \\, {\\left(1488 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 520 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} + {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4} + 7 \\, {\\left(3408 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{8} e^{\\left(8 \\, x^{2}\\right)} + 240 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} + 520 \\, {\\left(76 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} - {\\left(27312 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} + 520 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} - {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4} - 120 \\, {\\left(28 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 3 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{2} + 80 \\, {\\left(546 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} e^{\\left(7 \\, x^{2}\\right)} + 5 \\, {\\left(28 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{3} - 42 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right) e^{\\left(7 \\, x^{2}\\right)}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{4} + 2520 \\, {\\left(28 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 3 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{2} - {\\left(21488 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{8} e^{\\left(8 \\, x^{2}\\right)} - 10752 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} + 784 \\, {\\left(76 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} - 49 \\, {\\left(4848 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 520 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} + {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4} + {\\left(162608 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 15904 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} - 49 \\, {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)} + {\\left(2032 \\, x^{8} + 14112 \\, x^{6} + 26040 \\, x^{4} + 12600 \\, x^{2} + 735\\right)} e^{\\left(2 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{2} - 840 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} + 21 \\, {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)} + 14 \\, {\\left(4704 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} e^{\\left(7 \\, x^{2}\\right)} - 1400 \\, {\\left(28 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{3} + 3 \\, {\\left(3584 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} + 100 \\, {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)} - {\\left(1104 \\, x^{8} + 4816 \\, x^{6} + 5400 \\, x^{4} + 1500 \\, x^{2} + 45\\right)} e^{\\left(3 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{2} - 1680 \\, {\\left(42 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} e^{\\left(7 \\, x^{2}\\right)} + 5 \\, {\\left(28 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{3} - 42 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right) e^{\\left(7 \\, x^{2}\\right)}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right) - 14 \\, {\\left(336 \\, {\\left(2 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} e^{\\left(8 \\, x^{2}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right) - {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{7} e^{\\left(7 \\, x^{2}\\right)}\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{5} - 200 \\, {\\left(28 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{7} e^{\\left(7 \\, x^{2}\\right)} + {\\left(112 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} - 84 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{3} e^{\\left(7 \\, x^{2}\\right)} - {\\left(56 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} e^{\\left(8 \\, x^{2}\\right)} - 24 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{2} e^{\\left(8 \\, x^{2}\\right)} + 3 \\, {\\left(20 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)^{3} + 3 \\, {\\left(224 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{7} e^{\\left(7 \\, x^{2}\\right)} - 100 \\, {\\left(112 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{5} + {\\left(3584 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} + 500 \\, {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)} - {\\left(1104 \\, x^{8} + 4816 \\, x^{6} + 5400 \\, x^{4} + 1500 \\, x^{2} + 45\\right)} e^{\\left(3 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{3} + 60 \\, {\\left(56 \\, {\\left(2 \\, x^{8} + x^{6}\\right)} e^{\\left(7 \\, x^{2}\\right)} - 5 \\, {\\left(60 \\, x^{8} + 112 \\, x^{6} + 45 \\, x^{4} + 3 \\, x^{2}\\right)} e^{\\left(5 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right) - {\\left(448 \\, x^{8} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{6} e^{\\left(8 \\, x^{2}\\right)} + 240 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - 300 \\, {\\left(20 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} - {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{4} + 3 \\, {\\left(432 \\, x^{8} e^{\\left(8 \\, x^{2}\\right)} + 120 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)} - {\\left(3888 \\, x^{8} + 11200 \\, x^{6} + 7800 \\, x^{4} + 1200 \\, x^{2} + 15\\right)} e^{\\left(4 \\, x^{2}\\right)}\\right)} \\cos\\left(e^{\\left(x^{2}\\right)}\\right)^{2} - 60 \\, {\\left(76 \\, x^{8} + 84 \\, x^{6} + 15 \\, x^{4}\\right)} e^{\\left(6 \\, x^{2}\\right)}\\right)} \\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)} \\cos\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)\\right)} \\sin\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)\\right)} \\sin\\left(\\sin\\left(\\sin\\left(e^{\\left(x^{2}\\right)}\\right)\\right)\\right)$" ], "text/plain": [ "16*(224*(2*x^8*cos(e^(x^2))^6*e^(8*x^2)*sin(e^(x^2)) - (2*x^8 + x^6)*cos(e^(x^2))^7*e^(7*x^2))*cos(sin(e^(x^2)))^7 - 280*(112*(2*x^8 + x^6)*cos(e^(x^2))^7*e^(7*x^2) + (112*(2*x^8 + x^6)*e^(7*x^2) - (60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2))*cos(e^(x^2))^5 - 84*(2*x^8 + x^6)*cos(e^(x^2))^3*e^(7*x^2) - (224*x^8*cos(e^(x^2))^6*e^(8*x^2) - 24*x^8*cos(e^(x^2))^2*e^(8*x^2) + 3*(20*x^8*e^(8*x^2) - (76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^4)*sin(e^(x^2)))*cos(sin(e^(x^2)))^5 - 14*(3136*(2*x^8 + x^6)*cos(e^(x^2))^7*e^(7*x^2) + 500*(112*(2*x^8 + x^6)*e^(7*x^2) - (60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2))*cos(e^(x^2))^5 - (37184*(2*x^8 + x^6)*e^(7*x^2) + 500*(60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2) - (1104*x^8 + 4816*x^6 + 5400*x^4 + 1500*x^2 + 45)*e^(3*x^2))*cos(e^(x^2))^3 - 60*(56*(2*x^8 + x^6)*e^(7*x^2) - 5*(60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2))*cos(e^(x^2)) - (6272*x^8*cos(e^(x^2))^6*e^(8*x^2) - 240*x^8*e^(8*x^2) + 1500*(20*x^8*e^(8*x^2) - (76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^4 - 3*(3632*x^8*e^(8*x^2) + 120*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2) - (3888*x^8 + 11200*x^6 + 7800*x^4 + 1200*x^2 + 15)*e^(4*x^2))*cos(e^(x^2))^2 + 60*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*sin(e^(x^2)))*cos(sin(e^(x^2)))^3 + (46816*(2*x^8 + x^6)*cos(e^(x^2))^7*e^(7*x^2) + 3920*(112*(2*x^8 + x^6)*e^(7*x^2) - (60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2))*cos(e^(x^2))^5 - 14*(28336*(2*x^8 + x^6)*e^(7*x^2) - 500*(60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2) + (1104*x^8 + 4816*x^6 + 5400*x^4 + 1500*x^2 + 45)*e^(3*x^2))*cos(e^(x^2))^3 + (46816*(2*x^8 + x^6)*e^(7*x^2) - 3920*(60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2) - 14*(1104*x^8 + 4816*x^6 + 5400*x^4 + 1500*x^2 + 45)*e^(3*x^2) + (16*x^8 + 224*x^6 + 840*x^4 + 840*x^2 + 105)*e^(x^2))*cos(e^(x^2)) - (93632*x^8*cos(e^(x^2))^6*e^(8*x^2) + 3344*x^8*e^(8*x^2) + 11760*(20*x^8*e^(8*x^2) - (76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^4 - 42*(2608*x^8*e^(8*x^2) - 120*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2) + (3888*x^8 + 11200*x^6 + 7800*x^4 + 1200*x^2 + 15)*e^(4*x^2))*cos(e^(x^2))^2 - 784*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2) - 7*(3888*x^8 + 11200*x^6 + 7800*x^4 + 1200*x^2 + 15)*e^(4*x^2) + (2032*x^8 + 14112*x^6 + 26040*x^4 + 12600*x^2 + 735)*e^(2*x^2))*sin(e^(x^2)))*cos(sin(e^(x^2))) + (448*x^8*cos(e^(x^2))^8*cos(sin(e^(x^2)))^6*e^(8*x^2) - 3344*x^8*cos(e^(x^2))^8*e^(8*x^2) + 672*x^8*e^(8*x^2) - 784*(76*x^8*e^(8*x^2) - (76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^6 + 7*(10608*x^8*e^(8*x^2) - 520*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2) + (3888*x^8 + 11200*x^6 + 7800*x^4 + 1200*x^2 + 15)*e^(4*x^2))*cos(e^(x^2))^4 + 840*(20*x^8*cos(e^(x^2))^8*e^(8*x^2) - 60*x^8*cos(e^(x^2))^4*e^(8*x^2) + 84*(2*x^8 + x^6)*cos(e^(x^2))^5*e^(7*x^2)*sin(e^(x^2)) + (76*x^8*e^(8*x^2) - (76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^6)*cos(sin(e^(x^2)))^4 - (21488*x^8*e^(8*x^2) - 784*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2) - 49*(3888*x^8 + 11200*x^6 + 7800*x^4 + 1200*x^2 + 15)*e^(4*x^2) + (2032*x^8 + 14112*x^6 + 26040*x^4 + 12600*x^2 + 735)*e^(2*x^2))*cos(e^(x^2))^2 + 42*(208*x^8*cos(e^(x^2))^8*e^(8*x^2) + 240*x^8*e^(8*x^2) + 120*(76*x^8*e^(8*x^2) - (76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^6 - (3312*x^8*e^(8*x^2) + 520*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2) - (3888*x^8 + 11200*x^6 + 7800*x^4 + 1200*x^2 + 15)*e^(4*x^2))*cos(e^(x^2))^4 - 120*(28*x^8*e^(8*x^2) - 3*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^2 + 80*(126*(2*x^8 + x^6)*cos(e^(x^2))^5*e^(7*x^2) + 5*(28*(2*x^8 + x^6)*e^(7*x^2) - (60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2))*cos(e^(x^2))^3 - 42*(2*x^8 + x^6)*cos(e^(x^2))*e^(7*x^2))*sin(e^(x^2)))*cos(sin(e^(x^2)))^2 + 840*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2) - 21*(3888*x^8 + 11200*x^6 + 7800*x^4 + 1200*x^2 + 15)*e^(4*x^2) - 14*(4704*(2*x^8 + x^6)*cos(e^(x^2))^5*e^(7*x^2) - 200*(28*(2*x^8 + x^6)*e^(7*x^2) - (60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2))*cos(e^(x^2))^3 + 3*(224*(2*x^8 + x^6)*e^(7*x^2) + 100*(60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2) - (1104*x^8 + 4816*x^6 + 5400*x^4 + 1500*x^2 + 45)*e^(3*x^2))*cos(e^(x^2)))*sin(e^(x^2)))*sin(sin(e^(x^2))))*cos(sin(sin(e^(x^2)))) + 16*(16*x^8*cos(e^(x^2))^8*cos(sin(e^(x^2)))^8*e^(8*x^2) + 672*x^8*cos(e^(x^2))^8*e^(8*x^2) - 5040*x^8*e^(8*x^2) - 840*(76*x^8*e^(8*x^2) - (76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^6 + 56*(76*x^8*cos(e^(x^2))^8*e^(8*x^2) - 60*x^8*cos(e^(x^2))^4*e^(8*x^2) + 84*(2*x^8 + x^6)*cos(e^(x^2))^5*e^(7*x^2)*sin(e^(x^2)) + (76*x^8*e^(8*x^2) - (76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^6)*cos(sin(e^(x^2)))^6 - 21*(1488*x^8*e^(8*x^2) - 520*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2) + (3888*x^8 + 11200*x^6 + 7800*x^4 + 1200*x^2 + 15)*e^(4*x^2))*cos(e^(x^2))^4 + 7*(3408*x^8*cos(e^(x^2))^8*e^(8*x^2) + 240*x^8*e^(8*x^2) + 520*(76*x^8*e^(8*x^2) - (76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^6 - (27312*x^8*e^(8*x^2) + 520*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2) - (3888*x^8 + 11200*x^6 + 7800*x^4 + 1200*x^2 + 15)*e^(4*x^2))*cos(e^(x^2))^4 - 120*(28*x^8*e^(8*x^2) - 3*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^2 + 80*(546*(2*x^8 + x^6)*cos(e^(x^2))^5*e^(7*x^2) + 5*(28*(2*x^8 + x^6)*e^(7*x^2) - (60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2))*cos(e^(x^2))^3 - 42*(2*x^8 + x^6)*cos(e^(x^2))*e^(7*x^2))*sin(e^(x^2)))*cos(sin(e^(x^2)))^4 + 2520*(28*x^8*e^(8*x^2) - 3*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^2 - (21488*x^8*cos(e^(x^2))^8*e^(8*x^2) - 10752*x^8*e^(8*x^2) + 784*(76*x^8*e^(8*x^2) - (76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^6 - 49*(4848*x^8*e^(8*x^2) - 520*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2) + (3888*x^8 + 11200*x^6 + 7800*x^4 + 1200*x^2 + 15)*e^(4*x^2))*cos(e^(x^2))^4 + (162608*x^8*e^(8*x^2) - 15904*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2) - 49*(3888*x^8 + 11200*x^6 + 7800*x^4 + 1200*x^2 + 15)*e^(4*x^2) + (2032*x^8 + 14112*x^6 + 26040*x^4 + 12600*x^2 + 735)*e^(2*x^2))*cos(e^(x^2))^2 - 840*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2) + 21*(3888*x^8 + 11200*x^6 + 7800*x^4 + 1200*x^2 + 15)*e^(4*x^2) + 14*(4704*(2*x^8 + x^6)*cos(e^(x^2))^5*e^(7*x^2) - 1400*(28*(2*x^8 + x^6)*e^(7*x^2) - (60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2))*cos(e^(x^2))^3 + 3*(3584*(2*x^8 + x^6)*e^(7*x^2) + 100*(60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2) - (1104*x^8 + 4816*x^6 + 5400*x^4 + 1500*x^2 + 45)*e^(3*x^2))*cos(e^(x^2)))*sin(e^(x^2)))*cos(sin(e^(x^2)))^2 - 1680*(42*(2*x^8 + x^6)*cos(e^(x^2))^5*e^(7*x^2) + 5*(28*(2*x^8 + x^6)*e^(7*x^2) - (60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2))*cos(e^(x^2))^3 - 42*(2*x^8 + x^6)*cos(e^(x^2))*e^(7*x^2))*sin(e^(x^2)) - 14*(336*(2*x^8*cos(e^(x^2))^6*e^(8*x^2)*sin(e^(x^2)) - (2*x^8 + x^6)*cos(e^(x^2))^7*e^(7*x^2))*cos(sin(e^(x^2)))^5 - 200*(28*(2*x^8 + x^6)*cos(e^(x^2))^7*e^(7*x^2) + (112*(2*x^8 + x^6)*e^(7*x^2) - (60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2))*cos(e^(x^2))^5 - 84*(2*x^8 + x^6)*cos(e^(x^2))^3*e^(7*x^2) - (56*x^8*cos(e^(x^2))^6*e^(8*x^2) - 24*x^8*cos(e^(x^2))^2*e^(8*x^2) + 3*(20*x^8*e^(8*x^2) - (76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^4)*sin(e^(x^2)))*cos(sin(e^(x^2)))^3 + 3*(224*(2*x^8 + x^6)*cos(e^(x^2))^7*e^(7*x^2) - 100*(112*(2*x^8 + x^6)*e^(7*x^2) - (60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2))*cos(e^(x^2))^5 + (3584*(2*x^8 + x^6)*e^(7*x^2) + 500*(60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2) - (1104*x^8 + 4816*x^6 + 5400*x^4 + 1500*x^2 + 45)*e^(3*x^2))*cos(e^(x^2))^3 + 60*(56*(2*x^8 + x^6)*e^(7*x^2) - 5*(60*x^8 + 112*x^6 + 45*x^4 + 3*x^2)*e^(5*x^2))*cos(e^(x^2)) - (448*x^8*cos(e^(x^2))^6*e^(8*x^2) + 240*x^8*e^(8*x^2) - 300*(20*x^8*e^(8*x^2) - (76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*cos(e^(x^2))^4 + 3*(432*x^8*e^(8*x^2) + 120*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2) - (3888*x^8 + 11200*x^6 + 7800*x^4 + 1200*x^2 + 15)*e^(4*x^2))*cos(e^(x^2))^2 - 60*(76*x^8 + 84*x^6 + 15*x^4)*e^(6*x^2))*sin(e^(x^2)))*cos(sin(e^(x^2))))*sin(sin(e^(x^2))))*sin(sin(sin(e^(x^2))))" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "D.simplify_full()" ] }, { "cell_type": "code", "execution_count": null, "id": "09459ac4", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 10.0", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 5 }