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

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