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。
\[ \begin{equation}\begin{split}【1/1】求函数{({e}^{\frac{1}{x}}{(x{(sin(x))}^{\frac{1}{2}})}^{\frac{1}{2}})}^{\frac{1}{2}} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x^{\frac{1}{4}}{e}^{(\frac{\frac{1}{2}}{x})}sin^{\frac{1}{8}}(x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( x^{\frac{1}{4}}{e}^{(\frac{\frac{1}{2}}{x})}sin^{\frac{1}{8}}(x)\right)}{dx}\\=&\frac{\frac{1}{4}{e}^{(\frac{\frac{1}{2}}{x})}sin^{\frac{1}{8}}(x)}{x^{\frac{3}{4}}} + x^{\frac{1}{4}}({e}^{(\frac{\frac{1}{2}}{x})}((\frac{\frac{1}{2}*-1}{x^{2}})ln(e) + \frac{(\frac{\frac{1}{2}}{x})(0)}{(e)}))sin^{\frac{1}{8}}(x) + \frac{x^{\frac{1}{4}}{e}^{(\frac{\frac{1}{2}}{x})}*\frac{1}{8}cos(x)}{sin^{\frac{7}{8}}(x)}\\=&\frac{x^{\frac{1}{4}}{e}^{(\frac{\frac{1}{2}}{x})}cos(x)}{8sin^{\frac{7}{8}}(x)} - \frac{{e}^{(\frac{\frac{1}{2}}{x})}sin^{\frac{1}{8}}(x)}{2x^{\frac{7}{4}}} + \frac{{e}^{(\frac{\frac{1}{2}}{x})}sin^{\frac{1}{8}}(x)}{4x^{\frac{3}{4}}}\\ \end{split}\end{equation} \]

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