There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(1 + cos(x))}^{arctan(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (cos(x) + 1)^{arctan(x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (cos(x) + 1)^{arctan(x)}\right)}{dx}\\=&((cos(x) + 1)^{arctan(x)}(((\frac{(1)}{(1 + (x)^{2})}))ln(cos(x) + 1) + \frac{(arctan(x))(-sin(x) + 0)}{(cos(x) + 1)}))\\=&\frac{(cos(x) + 1)^{arctan(x)}ln(cos(x) + 1)}{(x^{2} + 1)} - \frac{(cos(x) + 1)^{arctan(x)}sin(x)arctan(x)}{(cos(x) + 1)}\\ \end{split}\end{equation} \]

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