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

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