There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{x}{6} + \frac{({(1 + {(4 - x)}^{2})}^{\frac{1}{2}})}{3}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{6}x + \frac{1}{3}(x^{2} - 8x + 17)^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{6}x + \frac{1}{3}(x^{2} - 8x + 17)^{\frac{1}{2}}\right)}{dx}\\=&\frac{1}{6} + \frac{1}{3}(\frac{\frac{1}{2}(2x - 8 + 0)}{(x^{2} - 8x + 17)^{\frac{1}{2}}})\\=&\frac{x}{3(x^{2} - 8x + 17)^{\frac{1}{2}}} - \frac{4}{3(x^{2} - 8x + 17)^{\frac{1}{2}}} + \frac{1}{6}\\ \end{split}\end{equation} \]

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