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

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