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

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