There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{x}{2}) + {({(12 - x)}^{2} + 144)}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}x + (x^{2} - 24x + 288)^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}x + (x^{2} - 24x + 288)^{\frac{1}{2}}\right)}{dx}\\=&\frac{1}{2} + (\frac{\frac{1}{2}(2x - 24 + 0)}{(x^{2} - 24x + 288)^{\frac{1}{2}}})\\=&\frac{x}{(x^{2} - 24x + 288)^{\frac{1}{2}}} - \frac{12}{(x^{2} - 24x + 288)^{\frac{1}{2}}} + \frac{1}{2}\\ \end{split}\end{equation} \]

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