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

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