There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 8sin(x){\frac{1}{((cos(x)))}}^{2} - cos(x){\frac{1}{((sin(x)))}}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{8sin(x)}{cos^{2}(x)} - \frac{cos(x)}{sin^{2}(x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{8sin(x)}{cos^{2}(x)} - \frac{cos(x)}{sin^{2}(x)}\right)}{dx}\\=&\frac{8cos(x)}{cos^{2}(x)} + \frac{8sin(x)*2sin(x)}{cos^{3}(x)} - \frac{-2cos(x)cos(x)}{sin^{3}(x)} - \frac{-sin(x)}{sin^{2}(x)}\\=&\frac{8}{cos(x)} + \frac{16sin^{2}(x)}{cos^{3}(x)} + \frac{2cos^{2}(x)}{sin^{3}(x)} + \frac{1}{sin(x)}\\ \end{split}\end{equation} \]

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