There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(\frac{(x - 1)(x - 2)}{((x - 3)(x - 4))})}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{(x - 1)^{\frac{1}{2}}(x - 2)^{\frac{1}{2}}}{(x - 3)^{\frac{1}{2}}(x - 4)^{\frac{1}{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{(x - 1)^{\frac{1}{2}}(x - 2)^{\frac{1}{2}}}{(x - 3)^{\frac{1}{2}}(x - 4)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{(\frac{\frac{1}{2}(1 + 0)}{(x - 1)^{\frac{1}{2}}})(x - 2)^{\frac{1}{2}}}{(x - 3)^{\frac{1}{2}}(x - 4)^{\frac{1}{2}}} + \frac{(x - 1)^{\frac{1}{2}}(\frac{\frac{1}{2}(1 + 0)}{(x - 2)^{\frac{1}{2}}})}{(x - 3)^{\frac{1}{2}}(x - 4)^{\frac{1}{2}}} + \frac{(x - 1)^{\frac{1}{2}}(x - 2)^{\frac{1}{2}}(\frac{\frac{-1}{2}(1 + 0)}{(x - 3)^{\frac{3}{2}}})}{(x - 4)^{\frac{1}{2}}} + \frac{(x - 1)^{\frac{1}{2}}(x - 2)^{\frac{1}{2}}(\frac{\frac{-1}{2}(1 + 0)}{(x - 4)^{\frac{3}{2}}})}{(x - 3)^{\frac{1}{2}}}\\=&\frac{(x - 2)^{\frac{1}{2}}}{2(x - 1)^{\frac{1}{2}}(x - 3)^{\frac{1}{2}}(x - 4)^{\frac{1}{2}}} + \frac{(x - 1)^{\frac{1}{2}}}{2(x - 2)^{\frac{1}{2}}(x - 3)^{\frac{1}{2}}(x - 4)^{\frac{1}{2}}} - \frac{(x - 1)^{\frac{1}{2}}(x - 2)^{\frac{1}{2}}}{2(x - 3)^{\frac{3}{2}}(x - 4)^{\frac{1}{2}}} - \frac{(x - 1)^{\frac{1}{2}}(x - 2)^{\frac{1}{2}}}{2(x - 3)^{\frac{1}{2}}(x - 4)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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