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

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