There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{{x}^{9}}{2688} - \frac{{x}^{7}}{210} + \frac{{x}^{3}ln(x)}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}x^{3}ln(x) - \frac{1}{210}x^{7} + \frac{1}{2688}x^{9}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}x^{3}ln(x) - \frac{1}{210}x^{7} + \frac{1}{2688}x^{9}\right)}{dx}\\=&\frac{1}{2}*3x^{2}ln(x) + \frac{\frac{1}{2}x^{3}}{(x)} - \frac{1}{210}*7x^{6} + \frac{1}{2688}*9x^{8}\\=&\frac{3x^{2}ln(x)}{2} + \frac{x^{2}}{2} - \frac{x^{6}}{30} + \frac{3x^{8}}{896}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{3x^{2}ln(x)}{2} + \frac{x^{2}}{2} - \frac{x^{6}}{30} + \frac{3x^{8}}{896}\right)}{dx}\\=&\frac{3*2xln(x)}{2} + \frac{3x^{2}}{2(x)} + \frac{2x}{2} - \frac{6x^{5}}{30} + \frac{3*8x^{7}}{896}\\=&3xln(x) + \frac{5x}{2} - \frac{x^{5}}{5} + \frac{3x^{7}}{112}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 3xln(x) + \frac{5x}{2} - \frac{x^{5}}{5} + \frac{3x^{7}}{112}\right)}{dx}\\=&3ln(x) + \frac{3x}{(x)} + \frac{5}{2} - \frac{5x^{4}}{5} + \frac{3*7x^{6}}{112}\\=&3ln(x) - x^{4} + \frac{3x^{6}}{16} + \frac{11}{2}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 3ln(x) - x^{4} + \frac{3x^{6}}{16} + \frac{11}{2}\right)}{dx}\\=&\frac{3}{(x)} - 4x^{3} + \frac{3*6x^{5}}{16} + 0\\=&\frac{3}{x} - 4x^{3} + \frac{9x^{5}}{8}\\ \end{split}\end{equation} \]

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