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