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