There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{1}{8}){(1 - {(cos(x))}^{2})}^{4}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{8}cos^{8}(x) - \frac{1}{2}cos^{6}(x) + \frac{3}{4}cos^{4}(x) - \frac{1}{2}cos^{2}(x) + \frac{1}{8}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{8}cos^{8}(x) - \frac{1}{2}cos^{6}(x) + \frac{3}{4}cos^{4}(x) - \frac{1}{2}cos^{2}(x) + \frac{1}{8}\right)}{dx}\\=&\frac{1}{8}*-8cos^{7}(x)sin(x) - \frac{1}{2}*-6cos^{5}(x)sin(x) + \frac{3}{4}*-4cos^{3}(x)sin(x) - \frac{1}{2}*-2cos(x)sin(x) + 0\\=&-sin(x)cos^{7}(x) + 3sin(x)cos^{5}(x) - 3sin(x)cos^{3}(x) + sin(x)cos(x)\\ \end{split}\end{equation} \]

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