There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {x}^{sin(sin(sin(sin(sin(sin(\frac{sin(-1)x}{3}))))))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {x}^{sin(sin(sin(sin(sin(sin(\frac{1}{3}xsin(-1)))))))}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {x}^{sin(sin(sin(sin(sin(sin(\frac{1}{3}xsin(-1)))))))}\right)}{dx}\\=&({x}^{sin(sin(sin(sin(sin(sin(\frac{1}{3}xsin(-1)))))))}((cos(sin(sin(sin(sin(sin(\frac{1}{3}xsin(-1)))))))cos(sin(sin(sin(sin(\frac{1}{3}xsin(-1))))))cos(sin(sin(sin(\frac{1}{3}xsin(-1)))))cos(sin(sin(\frac{1}{3}xsin(-1))))cos(sin(\frac{1}{3}xsin(-1)))cos(\frac{1}{3}xsin(-1))(\frac{1}{3}sin(-1) + \frac{1}{3}xcos(-1)*0))ln(x) + \frac{(sin(sin(sin(sin(sin(sin(\frac{1}{3}xsin(-1))))))))(1)}{(x)}))\\=&\frac{{x}^{sin(sin(sin(sin(sin(sin(\frac{1}{3}xsin(-1)))))))}ln(x)sin(-1)cos(sin(sin(sin(\frac{1}{3}xsin(-1)))))cos(\frac{1}{3}xsin(-1))cos(sin(sin(sin(sin(\frac{1}{3}xsin(-1))))))cos(sin(sin(\frac{1}{3}xsin(-1))))cos(sin(sin(sin(sin(sin(\frac{1}{3}xsin(-1)))))))cos(sin(\frac{1}{3}xsin(-1)))}{3} + \frac{{x}^{sin(sin(sin(sin(sin(sin(\frac{1}{3}xsin(-1)))))))}sin(sin(sin(sin(sin(sin(\frac{1}{3}xsin(-1)))))))}{x}\\ \end{split}\end{equation} \]

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