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

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