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

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