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。\[ \begin{equation}\begin{split}【1/1】求函数(3{x}^{2} + 2{({x}^{3} + 4{\frac{1}{x}}^{4})}^{\frac{1}{2}}){\frac{1}{(({x}^{3} - 4)({x}^{2} + 2))}}^{\frac{1}{2}} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{3x^{2}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} + \frac{2(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{3x^{2}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} + \frac{2(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}}\right)}{dx}\\=&3(\frac{\frac{-1}{2}(5x^{4} + 2*3x^{2} - 4*2x + 0)}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}})x^{2} + \frac{3*2x}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} + \frac{2(\frac{\frac{1}{2}(3x^{2} + \frac{4*-4}{x^{5}})}{(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}})}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} + 2(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}(\frac{\frac{-1}{2}(5x^{4} + 2*3x^{2} - 4*2x + 0)}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}})\\=&\frac{-15x^{6}}{2(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} - \frac{9x^{4}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} + \frac{12x^{3}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} + \frac{6x}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} + \frac{3x^{2}}{(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} - \frac{16}{(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}x^{5}} - \frac{5(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}x^{4}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} - \frac{6(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}x^{2}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} + \frac{8(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}x}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!