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

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