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

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