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

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