There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {({x}^{3} + 2)}^{5}cos(4x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{15}cos(4x) + 10x^{12}cos(4x) + 40x^{9}cos(4x) + 80x^{6}cos(4x) + 80x^{3}cos(4x) + 32cos(4x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{15}cos(4x) + 10x^{12}cos(4x) + 40x^{9}cos(4x) + 80x^{6}cos(4x) + 80x^{3}cos(4x) + 32cos(4x)\right)}{dx}\\=&15x^{14}cos(4x) + x^{15}*-sin(4x)*4 + 10*12x^{11}cos(4x) + 10x^{12}*-sin(4x)*4 + 40*9x^{8}cos(4x) + 40x^{9}*-sin(4x)*4 + 80*6x^{5}cos(4x) + 80x^{6}*-sin(4x)*4 + 80*3x^{2}cos(4x) + 80x^{3}*-sin(4x)*4 + 32*-sin(4x)*4\\=&15x^{14}cos(4x) - 4x^{15}sin(4x) + 120x^{11}cos(4x) - 40x^{12}sin(4x) + 360x^{8}cos(4x) - 160x^{9}sin(4x) + 480x^{5}cos(4x) - 320x^{6}sin(4x) + 240x^{2}cos(4x) - 320x^{3}sin(4x) - 128sin(4x)\\ \end{split}\end{equation} \]

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