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

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