本次共计算 1 个题目：每一题对 x 求 1 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数(144x - 144){\frac{1}{(\frac{-288x}{π} + 144{x}^{2}{π}^{2} + 144 + 25)}}^{\frac{1}{2}}{π}^{2} + \frac{12cos(\frac{x}{2})}{π} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{144π^{2}x}{(\frac{-288x}{π} + 144π^{2}x^{2} + 169)^{\frac{1}{2}}} - \frac{144π^{2}}{(\frac{-288x}{π} + 144π^{2}x^{2} + 169)^{\frac{1}{2}}} + \frac{12cos(\frac{1}{2}x)}{π}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{144π^{2}x}{(\frac{-288x}{π} + 144π^{2}x^{2} + 169)^{\frac{1}{2}}} - \frac{144π^{2}}{(\frac{-288x}{π} + 144π^{2}x^{2} + 169)^{\frac{1}{2}}} + \frac{12cos(\frac{1}{2}x)}{π}\right)}{dx}\\=&144(\frac{\frac{-1}{2}(\frac{-288}{π} + 144π^{2}*2x + 0)}{(\frac{-288x}{π} + 144π^{2}x^{2} + 169)^{\frac{3}{2}}})π^{2}x + \frac{144π^{2}}{(\frac{-288x}{π} + 144π^{2}x^{2} + 169)^{\frac{1}{2}}} - 144(\frac{\frac{-1}{2}(\frac{-288}{π} + 144π^{2}*2x + 0)}{(\frac{-288x}{π} + 144π^{2}x^{2} + 169)^{\frac{3}{2}}})π^{2} + 0 + \frac{12*-sin(\frac{1}{2}x)*\frac{1}{2}}{π}\\=& - \frac{20736π^{4}x^{2}}{(\frac{-288x}{π} + 144π^{2}x^{2} + 169)^{\frac{3}{2}}} + \frac{20736πx}{(\frac{-288x}{π} + 144π^{2}x^{2} + 169)^{\frac{3}{2}}} + \frac{20736π^{4}x}{(\frac{-288x}{π} + 144π^{2}x^{2} + 169)^{\frac{3}{2}}} + \frac{144π^{2}}{(\frac{-288x}{π} + 144π^{2}x^{2} + 169)^{\frac{1}{2}}} - \frac{20736π}{(\frac{-288x}{π} + 144π^{2}x^{2} + 169)^{\frac{3}{2}}} - \frac{6sin(\frac{1}{2}x)}{π}\\ \end{split}\end{equation} \]

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