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。
\[ \begin{equation}\begin{split}【1/1】求函数(1 + (sqrt(5)d{\frac{1}{10}}^{x}) + (\frac{5{d}^{2}}{(3 * {10}^{2}x)})){e}^{(sqrt(5)d{\frac{1}{10}}^{x})} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = {e}^{(d{\frac{1}{10}}^{x}sqrt(5))} + d{\frac{1}{10}}^{x}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}sqrt(5) + \frac{\frac{1}{60}d^{2}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}}{x}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {e}^{(d{\frac{1}{10}}^{x}sqrt(5))} + d{\frac{1}{10}}^{x}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}sqrt(5) + \frac{\frac{1}{60}d^{2}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}}{x}\right)}{dx}\\=&({e}^{(d{\frac{1}{10}}^{x}sqrt(5))}((d({\frac{1}{10}}^{x}((1)ln(\frac{1}{10}) + \frac{(x)(0)}{(\frac{1}{10})}))sqrt(5) + d{\frac{1}{10}}^{x}*0*\frac{1}{2}*5^{\frac{1}{2}})ln(e) + \frac{(d{\frac{1}{10}}^{x}sqrt(5))(0)}{(e)})) + d({\frac{1}{10}}^{x}((1)ln(\frac{1}{10}) + \frac{(x)(0)}{(\frac{1}{10})})){e}^{(d{\frac{1}{10}}^{x}sqrt(5))}sqrt(5) + d{\frac{1}{10}}^{x}({e}^{(d{\frac{1}{10}}^{x}sqrt(5))}((d({\frac{1}{10}}^{x}((1)ln(\frac{1}{10}) + \frac{(x)(0)}{(\frac{1}{10})}))sqrt(5) + d{\frac{1}{10}}^{x}*0*\frac{1}{2}*5^{\frac{1}{2}})ln(e) + \frac{(d{\frac{1}{10}}^{x}sqrt(5))(0)}{(e)}))sqrt(5) + d{\frac{1}{10}}^{x}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}*0*\frac{1}{2}*5^{\frac{1}{2}} + \frac{\frac{1}{60}d^{2}*-{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}}{x^{2}} + \frac{\frac{1}{60}d^{2}({e}^{(d{\frac{1}{10}}^{x}sqrt(5))}((d({\frac{1}{10}}^{x}((1)ln(\frac{1}{10}) + \frac{(x)(0)}{(\frac{1}{10})}))sqrt(5) + d{\frac{1}{10}}^{x}*0*\frac{1}{2}*5^{\frac{1}{2}})ln(e) + \frac{(d{\frac{1}{10}}^{x}sqrt(5))(0)}{(e)}))}{x}\\=&2d{\frac{1}{10}}^{x}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}ln(\frac{1}{10})sqrt(5) + d^{2}{\frac{1}{10}}^{(2x)}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}ln(\frac{1}{10})sqrt(5)^{2} + \frac{d^{3}{\frac{1}{10}}^{x}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}ln(\frac{1}{10})sqrt(5)}{60x} - \frac{d^{2}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}}{60x^{2}}\\ \end{split}\end{equation} \]

你的问题在这里没有得到解决？请到 热门难题 里面看看吧！