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

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