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。
\[ \begin{equation}\begin{split}【1/1】求函数x - \frac{({x}^{3} + 2{x}^{2} + 10x - 20)}{(3{x}^{2} + 4x + 10)} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x - \frac{x^{3}}{(3x^{2} + 4x + 10)} - \frac{2x^{2}}{(3x^{2} + 4x + 10)} - \frac{10x}{(3x^{2} + 4x + 10)} + \frac{20}{(3x^{2} + 4x + 10)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( x - \frac{x^{3}}{(3x^{2} + 4x + 10)} - \frac{2x^{2}}{(3x^{2} + 4x + 10)} - \frac{10x}{(3x^{2} + 4x + 10)} + \frac{20}{(3x^{2} + 4x + 10)}\right)}{dx}\\=&1 - (\frac{-(3*2x + 4 + 0)}{(3x^{2} + 4x + 10)^{2}})x^{3} - \frac{3x^{2}}{(3x^{2} + 4x + 10)} - 2(\frac{-(3*2x + 4 + 0)}{(3x^{2} + 4x + 10)^{2}})x^{2} - \frac{2*2x}{(3x^{2} + 4x + 10)} - 10(\frac{-(3*2x + 4 + 0)}{(3x^{2} + 4x + 10)^{2}})x - \frac{10}{(3x^{2} + 4x + 10)} + 20(\frac{-(3*2x + 4 + 0)}{(3x^{2} + 4x + 10)^{2}})\\=&\frac{6x^{4}}{(3x^{2} + 4x + 10)^{2}} + \frac{16x^{3}}{(3x^{2} + 4x + 10)^{2}} - \frac{3x^{2}}{(3x^{2} + 4x + 10)} + \frac{68x^{2}}{(3x^{2} + 4x + 10)^{2}} - \frac{4x}{(3x^{2} + 4x + 10)} - \frac{80x}{(3x^{2} + 4x + 10)^{2}} - \frac{10}{(3x^{2} + 4x + 10)} - \frac{80}{(3x^{2} + 4x + 10)^{2}} + 1\\ \end{split}\end{equation} \]

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