There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ({x}^{2} + 4x + 20)sqrt({x}^{2} + 12) + 4{x}^{2} + 16x - 48\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}sqrt(x^{2} + 12) + 4xsqrt(x^{2} + 12) + 20sqrt(x^{2} + 12) + 4x^{2} + 16x - 48\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{2}sqrt(x^{2} + 12) + 4xsqrt(x^{2} + 12) + 20sqrt(x^{2} + 12) + 4x^{2} + 16x - 48\right)}{dx}\\=&2xsqrt(x^{2} + 12) + \frac{x^{2}(2x + 0)*\frac{1}{2}}{(x^{2} + 12)^{\frac{1}{2}}} + 4sqrt(x^{2} + 12) + \frac{4x(2x + 0)*\frac{1}{2}}{(x^{2} + 12)^{\frac{1}{2}}} + \frac{20(2x + 0)*\frac{1}{2}}{(x^{2} + 12)^{\frac{1}{2}}} + 4*2x + 16 + 0\\=&2xsqrt(x^{2} + 12) + \frac{x^{3}}{(x^{2} + 12)^{\frac{1}{2}}} + 4sqrt(x^{2} + 12) + \frac{4x^{2}}{(x^{2} + 12)^{\frac{1}{2}}} + \frac{20x}{(x^{2} + 12)^{\frac{1}{2}}} + 8x + 16\\ \end{split}\end{equation} \]

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