There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ -({2}^{x} + 2)({2}^{x} + 1){\frac{1}{2}}^{x} - 1\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -{2}^{(3(x))} - 3 * {2}^{(2(x))} - 2 * {\frac{1}{2}}^{x} - 1\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -{2}^{(3(x))} - 3 * {2}^{(2(x))} - 2 * {\frac{1}{2}}^{x} - 1\right)}{dx}\\=&-({2}^{(3(x))}((3(1))ln(2) + \frac{(3(x))(0)}{(2)})) - 3({2}^{(2(x))}((2(1))ln(2) + \frac{(2(x))(0)}{(2)})) - 2({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})})) + 0\\=&-3 * {2}^{(3x)}ln(2) - 6 * {2}^{(2x)}ln(2) - 2 * {\frac{1}{2}}^{x}ln(\frac{1}{2})\\ \end{split}\end{equation} \]

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