There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (((log_{a}^{{e}^{{({x}^{2} + 5x)}^{\frac{1}{2}}}}) - ({e}^{{(ln(x))}^{\frac{1}{2}}})))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = log_{a}^{{e}^{(x^{2} + 5x)^{\frac{1}{2}}}} - {e}^{ln^{\frac{1}{2}}(x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{a}^{{e}^{(x^{2} + 5x)^{\frac{1}{2}}}} - {e}^{ln^{\frac{1}{2}}(x)}\right)}{dx}\\=&(\frac{(\frac{(({e}^{(x^{2} + 5x)^{\frac{1}{2}}}(((\frac{\frac{1}{2}(2x + 5)}{(x^{2} + 5x)^{\frac{1}{2}}}))ln(e) + \frac{((x^{2} + 5x)^{\frac{1}{2}})(0)}{(e)})))}{({e}^{(x^{2} + 5x)^{\frac{1}{2}}})} - \frac{(0)log_{a}^{{e}^{(x^{2} + 5x)^{\frac{1}{2}}}}}{(a)})}{(ln(a))}) - ({e}^{ln^{\frac{1}{2}}(x)}((\frac{\frac{1}{2}}{ln^{\frac{1}{2}}(x)(x)})ln(e) + \frac{(ln^{\frac{1}{2}}(x))(0)}{(e)}))\\=&\frac{x}{(x^{2} + 5x)^{\frac{1}{2}}ln(a)} + \frac{5}{2(x^{2} + 5x)^{\frac{1}{2}}ln(a)} - \frac{{e}^{ln^{\frac{1}{2}}(x)}}{2xln^{\frac{1}{2}}(x)}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！