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

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