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

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