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

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