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

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