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

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