There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ xsqrt(\frac{(x - 1)(x - 2)(x - 4)}{(x - 3)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = xsqrt(\frac{x^{3}}{(x - 3)} - \frac{7x^{2}}{(x - 3)} + \frac{14x}{(x - 3)} - \frac{8}{(x - 3)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xsqrt(\frac{x^{3}}{(x - 3)} - \frac{7x^{2}}{(x - 3)} + \frac{14x}{(x - 3)} - \frac{8}{(x - 3)})\right)}{dx}\\=&sqrt(\frac{x^{3}}{(x - 3)} - \frac{7x^{2}}{(x - 3)} + \frac{14x}{(x - 3)} - \frac{8}{(x - 3)}) + \frac{x((\frac{-(1 + 0)}{(x - 3)^{2}})x^{3} + \frac{3x^{2}}{(x - 3)} - 7(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2} - \frac{7*2x}{(x - 3)} + 14(\frac{-(1 + 0)}{(x - 3)^{2}})x + \frac{14}{(x - 3)} - 8(\frac{-(1 + 0)}{(x - 3)^{2}}))*\frac{1}{2}}{(\frac{x^{3}}{(x - 3)} - \frac{7x^{2}}{(x - 3)} + \frac{14x}{(x - 3)} - \frac{8}{(x - 3)})^{\frac{1}{2}}}\\=&sqrt(\frac{x^{3}}{(x - 3)} - \frac{7x^{2}}{(x - 3)} + \frac{14x}{(x - 3)} - \frac{8}{(x - 3)}) - \frac{x^{4}}{2(x - 3)^{2}(\frac{x^{3}}{(x - 3)} - \frac{7x^{2}}{(x - 3)} + \frac{14x}{(x - 3)} - \frac{8}{(x - 3)})^{\frac{1}{2}}} + \frac{3x^{3}}{2(x - 3)(\frac{x^{3}}{(x - 3)} - \frac{7x^{2}}{(x - 3)} + \frac{14x}{(x - 3)} - \frac{8}{(x - 3)})^{\frac{1}{2}}} + \frac{7x^{3}}{2(x - 3)^{2}(\frac{x^{3}}{(x - 3)} - \frac{7x^{2}}{(x - 3)} + \frac{14x}{(x - 3)} - \frac{8}{(x - 3)})^{\frac{1}{2}}} - \frac{7x^{2}}{(x - 3)(\frac{x^{3}}{(x - 3)} - \frac{7x^{2}}{(x - 3)} + \frac{14x}{(x - 3)} - \frac{8}{(x - 3)})^{\frac{1}{2}}} - \frac{7x^{2}}{(x - 3)^{2}(\frac{x^{3}}{(x - 3)} - \frac{7x^{2}}{(x - 3)} + \frac{14x}{(x - 3)} - \frac{8}{(x - 3)})^{\frac{1}{2}}} + \frac{7x}{(x - 3)(\frac{x^{3}}{(x - 3)} - \frac{7x^{2}}{(x - 3)} + \frac{14x}{(x - 3)} - \frac{8}{(x - 3)})^{\frac{1}{2}}} + \frac{4x}{(x - 3)^{2}(\frac{x^{3}}{(x - 3)} - \frac{7x^{2}}{(x - 3)} + \frac{14x}{(x - 3)} - \frac{8}{(x - 3)})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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