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。
\[ \begin{equation}\begin{split}【1/1】求函数sin(\frac{(1 + {x}^{4})}{({x}^{2} + cos({x}^{3}))}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin(\frac{x^{4}}{(x^{2} + cos(x^{3}))} + \frac{1}{(x^{2} + cos(x^{3}))})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(\frac{x^{4}}{(x^{2} + cos(x^{3}))} + \frac{1}{(x^{2} + cos(x^{3}))})\right)}{dx}\\=&cos(\frac{x^{4}}{(x^{2} + cos(x^{3}))} + \frac{1}{(x^{2} + cos(x^{3}))})((\frac{-(2x + -sin(x^{3})*3x^{2})}{(x^{2} + cos(x^{3}))^{2}})x^{4} + \frac{4x^{3}}{(x^{2} + cos(x^{3}))} + (\frac{-(2x + -sin(x^{3})*3x^{2})}{(x^{2} + cos(x^{3}))^{2}}))\\=&\frac{-2x^{5}cos(\frac{x^{4}}{(x^{2} + cos(x^{3}))} + \frac{1}{(x^{2} + cos(x^{3}))})}{(x^{2} + cos(x^{3}))^{2}} + \frac{3x^{6}sin(x^{3})cos(\frac{x^{4}}{(x^{2} + cos(x^{3}))} + \frac{1}{(x^{2} + cos(x^{3}))})}{(x^{2} + cos(x^{3}))^{2}} + \frac{4x^{3}cos(\frac{x^{4}}{(x^{2} + cos(x^{3}))} + \frac{1}{(x^{2} + cos(x^{3}))})}{(x^{2} + cos(x^{3}))} - \frac{2xcos(\frac{x^{4}}{(x^{2} + cos(x^{3}))} + \frac{1}{(x^{2} + cos(x^{3}))})}{(x^{2} + cos(x^{3}))^{2}} + \frac{3x^{2}sin(x^{3})cos(\frac{x^{4}}{(x^{2} + cos(x^{3}))} + \frac{1}{(x^{2} + cos(x^{3}))})}{(x^{2} + cos(x^{3}))^{2}}\\ \end{split}\end{equation} \]

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