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

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