Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ x{(\frac{(x - 1)(x - 2)}{((x - 3)(x - 4))})}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \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}}x\\&\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}}x\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}}})x + (\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}\\=&\frac{-x^{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)^{2}(x - 4)} - \frac{x^{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 - 4)^{2}(x - 3)} + \frac{x^{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)(x - 3)} + \frac{3x^{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{3x^{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{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)(x - 4)} - \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 - 3)^{2}(x - 4)} - \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)^{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}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-x^{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)^{2}(x - 4)} - \frac{x^{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 - 4)^{2}(x - 3)} + \frac{x^{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)(x - 3)} + \frac{3x^{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{3x^{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{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)(x - 4)} - \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 - 3)^{2}(x - 4)} - \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)^{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}}\right)}{dx}\\=&\frac{-(\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{3}{2}}})x^{3}}{2(x - 3)^{2}(x - 4)} - \frac{(\frac{-2(1 + 0)}{(x - 3)^{3}})x^{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 - 4)} - \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{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)^{2}} - \frac{3x^{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{(\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{3}{2}}})x^{3}}{2(x - 4)^{2}(x - 3)} - \frac{(\frac{-2(1 + 0)}{(x - 4)^{3}})x^{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)} - \frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x^{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 - 4)^{2}} - \frac{3x^{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{(\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{3}{2}}})x^{2}}{(x - 4)(x - 3)} + \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{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)} + \frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x^{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)} + \frac{2x}{(\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{3(\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{3}{2}}})x^{2}}{2(x - 3)^{2}(x - 4)} + \frac{3(\frac{-2(1 + 0)}{(x - 3)^{3}})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)} + \frac{3(\frac{-(1 + 0)}{(x - 4)^{2}})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}} + \frac{3*2x}{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{3(\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{3}{2}}})x^{2}}{2(x - 4)^{2}(x - 3)} + \frac{3(\frac{-2(1 + 0)}{(x - 4)^{3}})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)} + \frac{3(\frac{-(1 + 0)}{(x - 3)^{2}})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}} + \frac{3*2x}{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{3(\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{3}{2}}})x}{2(x - 3)(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 3)^{2}})x}{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)} - \frac{3(\frac{-(1 + 0)}{(x - 4)^{2}})x}{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)} - \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)} - \frac{(\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{3}{2}}})x}{(x - 3)^{2}(x - 4)} - \frac{(\frac{-2(1 + 0)}{(x - 3)^{3}})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)} - \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(\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}} - \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{(\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{3}{2}}})x}{(x - 4)^{2}(x - 3)} - \frac{(\frac{-2(1 + 0)}{(x - 4)^{3}})x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)} - \frac{(\frac{-(1 + 0)}{(x - 3)^{2}})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)^{2}} - \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{\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^{5}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{4}(x - 4)^{2}} - \frac{x^{5}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{3}} + \frac{x^{4}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{2}(x - 3)^{3}} + \frac{3x^{4}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{4}(x - 4)^{2}} + \frac{3x^{4}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{3}} + \frac{x^{4}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{2}} - \frac{x^{5}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{3}} - \frac{x^{5}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{4}(x - 3)^{2}} + \frac{x^{3}}{(x - 3)^{3}(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)} + \frac{x^{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 - 4)^{2}(x - 3)^{2}} - \frac{3x^{2}}{2(x - 3)^{2}(x - 4)(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}} + \frac{3x^{4}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{3}} + \frac{3x^{4}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{4}(x - 3)^{2}} + \frac{x^{4}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{2}} - \frac{13x^{3}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{4}(x - 4)^{2}} - \frac{13x^{3}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{3}} + \frac{x^{3}}{(x - 4)^{3}(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)} + \frac{x^{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)^{2}(x - 4)^{2}} - \frac{3x^{2}}{2(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{3x^{3}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{2}} - \frac{15x^{3}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{2}} - \frac{x^{3}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{2}(x - 3)^{2}} - \frac{3x^{3}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{2}(x - 3)^{3}} + \frac{3x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{2}(x - 3)^{2}} - \frac{x^{2}}{(x - 4)^{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)} - \frac{3x^{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{2x}{(x - 4)(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{11x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{2}} - \frac{13x^{3}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{3}} - \frac{13x^{3}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{4}(x - 3)^{2}} + \frac{17x^{2}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{2}} - \frac{3x^{2}}{(x - 3)^{3}(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)} - \frac{3x^{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)^{2}} + \frac{3x}{(x - 3)^{2}(x - 4)(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}} + \frac{3x^{2}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{4}(x - 4)^{2}} + \frac{3x^{2}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{3}} + \frac{x^{2}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{2}(x - 3)^{3}} + \frac{3x^{2}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{3}} + \frac{3x^{2}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{4}(x - 3)^{2}} - \frac{3x^{2}}{(x - 4)^{3}(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)} - \frac{3x^{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)^{2}} + \frac{3x}{(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{3x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{2}(x - 4)^{2}} - \frac{9x}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{2}(x - 4)^{2}} - \frac{3x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{2}} - \frac{3x}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{2}} + \frac{3x}{2(x - 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 - 4)} + \frac{3x}{(\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{3x^{3}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{2}(x - 4)^{3}} - \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{4}(x - 4)^{2}} - \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{3}} + \frac{9x^{2}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{2}(x - 4)^{3}} - \frac{3x}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{2}(x - 4)^{3}} - \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{3}} - \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{4}(x - 3)^{2}} + \frac{2x}{(x - 3)^{3}(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)} + \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)^{2}(x - 3)^{2}} + \frac{2x}{(x - 4)^{3}(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{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 - 3)^{2}(x - 4)^{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 - 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{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{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{3}{(\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} \]