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

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