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

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