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

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