There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(1 + ({6}^{x}))}^{\frac{1}{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ({6}^{x} + 1)^{\frac{1}{x}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ({6}^{x} + 1)^{\frac{1}{x}}\right)}{dx}\\=&(({6}^{x} + 1)^{\frac{1}{x}}((\frac{-1}{x^{2}})ln({6}^{x} + 1) + \frac{(\frac{1}{x})(({6}^{x}((1)ln(6) + \frac{(x)(0)}{(6)})) + 0)}{({6}^{x} + 1)}))\\=&\frac{-({6}^{x} + 1)^{\frac{1}{x}}ln({6}^{x} + 1)}{x^{2}} + \frac{{6}^{x}({6}^{x} + 1)^{\frac{1}{x}}ln(6)}{({6}^{x} + 1)x}\\ \end{split}\end{equation} \]

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