There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt(({x}^{2} + 16)sqrt({x}^{2} - 4x + 16) + 4{x}^{2} - 32x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(x^{2}sqrt(x^{2} - 4x + 16) + 16sqrt(x^{2} - 4x + 16) + 4x^{2} - 32x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(x^{2}sqrt(x^{2} - 4x + 16) + 16sqrt(x^{2} - 4x + 16) + 4x^{2} - 32x)\right)}{dx}\\=&\frac{(2xsqrt(x^{2} - 4x + 16) + \frac{x^{2}(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 16)^{\frac{1}{2}}} + \frac{16(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 16)^{\frac{1}{2}}} + 4*2x - 32)*\frac{1}{2}}{(x^{2}sqrt(x^{2} - 4x + 16) + 16sqrt(x^{2} - 4x + 16) + 4x^{2} - 32x)^{\frac{1}{2}}}\\=&\frac{xsqrt(x^{2} - 4x + 16)}{(x^{2}sqrt(x^{2} - 4x + 16) + 16sqrt(x^{2} - 4x + 16) + 4x^{2} - 32x)^{\frac{1}{2}}} + \frac{x^{3}}{2(x^{2} - 4x + 16)^{\frac{1}{2}}(x^{2}sqrt(x^{2} - 4x + 16) + 16sqrt(x^{2} - 4x + 16) + 4x^{2} - 32x)^{\frac{1}{2}}} - \frac{x^{2}}{(x^{2} - 4x + 16)^{\frac{1}{2}}(x^{2}sqrt(x^{2} - 4x + 16) + 16sqrt(x^{2} - 4x + 16) + 4x^{2} - 32x)^{\frac{1}{2}}} + \frac{8x}{(x^{2} - 4x + 16)^{\frac{1}{2}}(x^{2}sqrt(x^{2} - 4x + 16) + 16sqrt(x^{2} - 4x + 16) + 4x^{2} - 32x)^{\frac{1}{2}}} - \frac{16}{(x^{2} - 4x + 16)^{\frac{1}{2}}(x^{2}sqrt(x^{2} - 4x + 16) + 16sqrt(x^{2} - 4x + 16) + 4x^{2} - 32x)^{\frac{1}{2}}} + \frac{4x}{(x^{2}sqrt(x^{2} - 4x + 16) + 16sqrt(x^{2} - 4x + 16) + 4x^{2} - 32x)^{\frac{1}{2}}} - \frac{16}{(x^{2}sqrt(x^{2} - 4x + 16) + 16sqrt(x^{2} - 4x + 16) + 4x^{2} - 32x)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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