There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({2}^{(x + 1)}ln(x))}{({4}^{x} + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{2}^{(x + 1)}ln(x)}{({4}^{x} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{{2}^{(x + 1)}ln(x)}{({4}^{x} + 1)}\right)}{dx}\\=&(\frac{-(({4}^{x}((1)ln(4) + \frac{(x)(0)}{(4)})) + 0)}{({4}^{x} + 1)^{2}}){2}^{(x + 1)}ln(x) + \frac{({2}^{(x + 1)}((1 + 0)ln(2) + \frac{(x + 1)(0)}{(2)}))ln(x)}{({4}^{x} + 1)} + \frac{{2}^{(x + 1)}}{({4}^{x} + 1)(x)}\\=&\frac{-{4}^{(2x)}ln(4)ln(x)}{({4}^{x} + 1)^{2}} + \frac{{2}^{(x + 1)}ln(2)ln(x)}{({4}^{x} + 1)} + \frac{{2}^{(x + 1)}}{({4}^{x} + 1)x}\\ \end{split}\end{equation} \]

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