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

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