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