There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt(\frac{(x - 2)(x - 3)}{(x - 4)(x - 5)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})\right)}{dx}\\=&\frac{(\frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{(x - 5)} + \frac{(\frac{-(1 + 0)}{(x - 5)^{2}})x^{2}}{(x - 4)} + \frac{2x}{(x - 4)(x - 5)} - \frac{5(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(x - 5)} - \frac{5(\frac{-(1 + 0)}{(x - 5)^{2}})x}{(x - 4)} - \frac{5}{(x - 4)(x - 5)} + \frac{6(\frac{-(1 + 0)}{(x - 4)^{2}})}{(x - 5)} + \frac{6(\frac{-(1 + 0)}{(x - 5)^{2}})}{(x - 4)})*\frac{1}{2}}{(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}}\\=&\frac{-x^{2}}{2(x - 5)(x - 4)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} - \frac{x^{2}}{2(x - 4)(x - 5)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} + \frac{x}{(x - 4)(x - 5)(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} + \frac{5x}{2(x - 5)(x - 4)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} + \frac{5x}{2(x - 4)(x - 5)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} - \frac{3}{(x - 5)(x - 4)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} - \frac{3}{(x - 4)(x - 5)^{2}(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}} - \frac{5}{2(x - 5)(x - 4)(\frac{x^{2}}{(x - 4)(x - 5)} - \frac{5x}{(x - 4)(x - 5)} + \frac{6}{(x - 4)(x - 5)})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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