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

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