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

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