There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{{x}^{3}}{ln(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{3}}{ln(x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{3}}{ln(x)}\right)}{dx}\\=&\frac{3x^{2}}{ln(x)} + \frac{x^{3}*-1}{ln^{2}(x)(x)}\\=&\frac{3x^{2}}{ln(x)} - \frac{x^{2}}{ln^{2}(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{3x^{2}}{ln(x)} - \frac{x^{2}}{ln^{2}(x)}\right)}{dx}\\=&\frac{3*2x}{ln(x)} + \frac{3x^{2}*-1}{ln^{2}(x)(x)} - \frac{2x}{ln^{2}(x)} - \frac{x^{2}*-2}{ln^{3}(x)(x)}\\=&\frac{6x}{ln(x)} - \frac{5x}{ln^{2}(x)} + \frac{2x}{ln^{3}(x)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{6x}{ln(x)} - \frac{5x}{ln^{2}(x)} + \frac{2x}{ln^{3}(x)}\right)}{dx}\\=&\frac{6}{ln(x)} + \frac{6x*-1}{ln^{2}(x)(x)} - \frac{5}{ln^{2}(x)} - \frac{5x*-2}{ln^{3}(x)(x)} + \frac{2}{ln^{3}(x)} + \frac{2x*-3}{ln^{4}(x)(x)}\\=&\frac{6}{ln(x)} - \frac{11}{ln^{2}(x)} + \frac{12}{ln^{3}(x)} - \frac{6}{ln^{4}(x)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{6}{ln(x)} - \frac{11}{ln^{2}(x)} + \frac{12}{ln^{3}(x)} - \frac{6}{ln^{4}(x)}\right)}{dx}\\=&\frac{6*-1}{ln^{2}(x)(x)} - \frac{11*-2}{ln^{3}(x)(x)} + \frac{12*-3}{ln^{4}(x)(x)} - \frac{6*-4}{ln^{5}(x)(x)}\\=&\frac{-6}{xln^{2}(x)} + \frac{22}{xln^{3}(x)} - \frac{36}{xln^{4}(x)} + \frac{24}{xln^{5}(x)}\\ \end{split}\end{equation} \]

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