There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{-x{e}^{(-4x)}}{4} + \frac{{e}^{(-4x)}}{16}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-1}{4}x{e}^{(-4x)} + \frac{1}{16}{e}^{(-4x)}\right)}{dx}\\=&\frac{-1}{4}{e}^{(-4x)} - \frac{1}{4}x({e}^{(-4x)}((-4)ln(e) + \frac{(-4x)(0)}{(e)})) + \frac{1}{16}({e}^{(-4x)}((-4)ln(e) + \frac{(-4x)(0)}{(e)}))\\=&\frac{-{e}^{(-4x)}}{2} + x{e}^{(-4x)}\\ \end{split}\end{equation} \]

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