本次共计算 2 个题目：每一题对 x 求 1 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/2】求函数\frac{10{e}^{(\frac{x}{2})}(6sin(\frac{3x}{5}) + 5cos(\frac{3x}{5}))}{61} + C 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{60}{61}{e}^{(\frac{1}{2}x)}sin(\frac{3}{5}x) + \frac{50}{61}{e}^{(\frac{1}{2}x)}cos(\frac{3}{5}x) + C\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{60}{61}{e}^{(\frac{1}{2}x)}sin(\frac{3}{5}x) + \frac{50}{61}{e}^{(\frac{1}{2}x)}cos(\frac{3}{5}x) + C\right)}{dx}\\=&\frac{60}{61}({e}^{(\frac{1}{2}x)}((\frac{1}{2})ln(e) + \frac{(\frac{1}{2}x)(0)}{(e)}))sin(\frac{3}{5}x) + \frac{60}{61}{e}^{(\frac{1}{2}x)}cos(\frac{3}{5}x)*\frac{3}{5} + \frac{50}{61}({e}^{(\frac{1}{2}x)}((\frac{1}{2})ln(e) + \frac{(\frac{1}{2}x)(0)}{(e)}))cos(\frac{3}{5}x) + \frac{50}{61}{e}^{(\frac{1}{2}x)}*-sin(\frac{3}{5}x)*\frac{3}{5} + 0\\=&{e}^{(\frac{1}{2}x)}cos(\frac{3}{5}x)\\ \end{split}\end{equation} \]

\[ \begin{equation}\begin{split}【2/2】求函数\frac{10{e}^{(\frac{x}{2})}(5sin(\frac{3x}{5}) - 6cos(\frac{3x}{5}))}{61} + C 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{50}{61}{e}^{(\frac{1}{2}x)}sin(\frac{3}{5}x) - \frac{60}{61}{e}^{(\frac{1}{2}x)}cos(\frac{3}{5}x) + C\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{50}{61}{e}^{(\frac{1}{2}x)}sin(\frac{3}{5}x) - \frac{60}{61}{e}^{(\frac{1}{2}x)}cos(\frac{3}{5}x) + C\right)}{dx}\\=&\frac{50}{61}({e}^{(\frac{1}{2}x)}((\frac{1}{2})ln(e) + \frac{(\frac{1}{2}x)(0)}{(e)}))sin(\frac{3}{5}x) + \frac{50}{61}{e}^{(\frac{1}{2}x)}cos(\frac{3}{5}x)*\frac{3}{5} - \frac{60}{61}({e}^{(\frac{1}{2}x)}((\frac{1}{2})ln(e) + \frac{(\frac{1}{2}x)(0)}{(e)}))cos(\frac{3}{5}x) - \frac{60}{61}{e}^{(\frac{1}{2}x)}*-sin(\frac{3}{5}x)*\frac{3}{5} + 0\\=&{e}^{(\frac{1}{2}x)}sin(\frac{3}{5}x)\\ \end{split}\end{equation} \]

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