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

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