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

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