There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({x}^{2})}{(1 + {x}^{2}sqrt(1 + {x}^{2}))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{2}}{(x^{2}sqrt(x^{2} + 1) + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{2}}{(x^{2}sqrt(x^{2} + 1) + 1)}\right)}{dx}\\=&(\frac{-(2xsqrt(x^{2} + 1) + \frac{x^{2}(2x + 0)*\frac{1}{2}}{(x^{2} + 1)^{\frac{1}{2}}} + 0)}{(x^{2}sqrt(x^{2} + 1) + 1)^{2}})x^{2} + \frac{2x}{(x^{2}sqrt(x^{2} + 1) + 1)}\\=&\frac{-2x^{3}sqrt(x^{2} + 1)}{(x^{2}sqrt(x^{2} + 1) + 1)^{2}} - \frac{x^{5}}{(x^{2}sqrt(x^{2} + 1) + 1)^{2}(x^{2} + 1)^{\frac{1}{2}}} + \frac{2x}{(x^{2}sqrt(x^{2} + 1) + 1)}\\ \end{split}\end{equation} \]

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