There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{2x(4 + {x}^{2})}{sqrt(16 + {x}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{8x}{sqrt(x^{2} + 16)} + \frac{2x^{3}}{sqrt(x^{2} + 16)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{8x}{sqrt(x^{2} + 16)} + \frac{2x^{3}}{sqrt(x^{2} + 16)}\right)}{dx}\\=&\frac{8}{sqrt(x^{2} + 16)} + \frac{8x*-(2x + 0)*\frac{1}{2}}{(x^{2} + 16)(x^{2} + 16)^{\frac{1}{2}}} + \frac{2*3x^{2}}{sqrt(x^{2} + 16)} + \frac{2x^{3}*-(2x + 0)*\frac{1}{2}}{(x^{2} + 16)(x^{2} + 16)^{\frac{1}{2}}}\\=&\frac{8}{sqrt(x^{2} + 16)} - \frac{8x^{2}}{(x^{2} + 16)^{\frac{3}{2}}} + \frac{6x^{2}}{sqrt(x^{2} + 16)} - \frac{2x^{4}}{(x^{2} + 16)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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