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

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