There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ lg(arctan(arccos(arcsin(sin(tan(cot(cosh(sinh(sqrt(x))))))))))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( lg(arctan(arccos(arcsin(sin(tan(cot(cosh(sinh(sqrt(x))))))))))\right)}{dx}\\=&\frac{(\frac{((\frac{-((\frac{(cos(tan(cot(cosh(sinh(sqrt(x))))))sec^{2}(cot(cosh(sinh(sqrt(x)))))(\frac{-csc^{2}(cosh(sinh(sqrt(x))))sinh(sinh(sqrt(x)))cosh(sqrt(x))*\frac{1}{2}}{(x)^{\frac{1}{2}}}))}{((1 - (sin(tan(cot(cosh(sinh(sqrt(x)))))))^{2})^{\frac{1}{2}})}))}{((1 - (arcsin(sin(tan(cot(cosh(sinh(sqrt(x))))))))^{2})^{\frac{1}{2}})}))}{(1 + (arccos(arcsin(sin(tan(cot(cosh(sinh(sqrt(x)))))))))^{2})})}{ln{10}(arctan(arccos(arcsin(sin(tan(cot(cosh(sinh(sqrt(x))))))))))}\\=&\frac{cos(tan(cot(cosh(sinh(sqrt(x))))))sec^{2}(cot(cosh(sinh(sqrt(x)))))csc^{2}(cosh(sinh(sqrt(x))))sinh(sinh(sqrt(x)))cosh(sqrt(x))}{2(-arcsin^{2}(sin(tan(cot(cosh(sinh(sqrt(x))))))) + 1)^{\frac{1}{2}}(-sin^{2}(tan(cot(cosh(sinh(sqrt(x)))))) + 1)^{\frac{1}{2}}(arccos^{2}(arcsin(sin(tan(cot(cosh(sinh(sqrt(x)))))))) + 1)x^{\frac{1}{2}}ln{10}arctan(arccos(arcsin(sin(tan(cot(cosh(sinh(sqrt(x)))))))))}\\ \end{split}\end{equation} \]

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