There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {({5}^{2} + {(\frac{12(π - x)}{π})}^{2})}^{\frac{1}{2}} + \frac{24sin(\frac{x}{2})}{π}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (\frac{-288x}{π} + \frac{144x^{2}}{π^{2}} + 169)^{\frac{1}{2}} + \frac{24sin(\frac{1}{2}x)}{π}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (\frac{-288x}{π} + \frac{144x^{2}}{π^{2}} + 169)^{\frac{1}{2}} + \frac{24sin(\frac{1}{2}x)}{π}\right)}{dx}\\=&(\frac{\frac{1}{2}(\frac{-288}{π} + \frac{144*2x}{π^{2}} + 0)}{(\frac{-288x}{π} + \frac{144x^{2}}{π^{2}} + 169)^{\frac{1}{2}}}) + \frac{24cos(\frac{1}{2}x)*\frac{1}{2}}{π}\\=&\frac{144x}{(\frac{-288x}{π} + \frac{144x^{2}}{π^{2}} + 169)^{\frac{1}{2}}π^{2}} - \frac{144}{(\frac{-288x}{π} + \frac{144x^{2}}{π^{2}} + 169)^{\frac{1}{2}}π} + \frac{12cos(\frac{1}{2}x)}{π}\\ \end{split}\end{equation} \]

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