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

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