There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(x + {(cos(x))}^{2})}^{5}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 5x^{4}cos^{2}(x) + 10x^{3}cos^{4}(x) + 10x^{2}cos^{6}(x) + 5xcos^{8}(x) + x^{5} + cos^{10}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 5x^{4}cos^{2}(x) + 10x^{3}cos^{4}(x) + 10x^{2}cos^{6}(x) + 5xcos^{8}(x) + x^{5} + cos^{10}(x)\right)}{dx}\\=&5*4x^{3}cos^{2}(x) + 5x^{4}*-2cos(x)sin(x) + 10*3x^{2}cos^{4}(x) + 10x^{3}*-4cos^{3}(x)sin(x) + 10*2xcos^{6}(x) + 10x^{2}*-6cos^{5}(x)sin(x) + 5cos^{8}(x) + 5x*-8cos^{7}(x)sin(x) + 5x^{4} + -10cos^{9}(x)sin(x)\\=&20x^{3}cos^{2}(x) - 10x^{4}sin(x)cos(x) + 30x^{2}cos^{4}(x) - 40x^{3}sin(x)cos^{3}(x) + 20xcos^{6}(x) - 60x^{2}sin(x)cos^{5}(x) + 5cos^{8}(x) - 40xsin(x)cos^{7}(x) + 5x^{4} - 10sin(x)cos^{9}(x)\\ \end{split}\end{equation} \]

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