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

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