There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ({x}^{n})(ln(x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {x}^{n}ln(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {x}^{n}ln(x)\right)}{dx}\\=&({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)}))ln(x) + \frac{{x}^{n}}{(x)}\\=&\frac{n{x}^{n}ln(x)}{x} + \frac{{x}^{n}}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{n{x}^{n}ln(x)}{x} + \frac{{x}^{n}}{x}\right)}{dx}\\=&\frac{n*-{x}^{n}ln(x)}{x^{2}} + \frac{n({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)}))ln(x)}{x} + \frac{n{x}^{n}}{x(x)} + \frac{-{x}^{n}}{x^{2}} + \frac{({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)}))}{x}\\=&\frac{-n{x}^{n}ln(x)}{x^{2}} + \frac{n^{2}{x}^{n}ln(x)}{x^{2}} + \frac{2n{x}^{n}}{x^{2}} - \frac{{x}^{n}}{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-n{x}^{n}ln(x)}{x^{2}} + \frac{n^{2}{x}^{n}ln(x)}{x^{2}} + \frac{2n{x}^{n}}{x^{2}} - \frac{{x}^{n}}{x^{2}}\right)}{dx}\\=&\frac{-n*-2{x}^{n}ln(x)}{x^{3}} - \frac{n({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)}))ln(x)}{x^{2}} - \frac{n{x}^{n}}{x^{2}(x)} + \frac{n^{2}*-2{x}^{n}ln(x)}{x^{3}} + \frac{n^{2}({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)}))ln(x)}{x^{2}} + \frac{n^{2}{x}^{n}}{x^{2}(x)} + \frac{2n*-2{x}^{n}}{x^{3}} + \frac{2n({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)}))}{x^{2}} - \frac{-2{x}^{n}}{x^{3}} - \frac{({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)}))}{x^{2}}\\=&\frac{2n{x}^{n}ln(x)}{x^{3}} - \frac{3n^{2}{x}^{n}ln(x)}{x^{3}} + \frac{n^{3}{x}^{n}ln(x)}{x^{3}} - \frac{6n{x}^{n}}{x^{3}} + \frac{3n^{2}{x}^{n}}{x^{3}} + \frac{2{x}^{n}}{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2n{x}^{n}ln(x)}{x^{3}} - \frac{3n^{2}{x}^{n}ln(x)}{x^{3}} + \frac{n^{3}{x}^{n}ln(x)}{x^{3}} - \frac{6n{x}^{n}}{x^{3}} + \frac{3n^{2}{x}^{n}}{x^{3}} + \frac{2{x}^{n}}{x^{3}}\right)}{dx}\\=&\frac{2n*-3{x}^{n}ln(x)}{x^{4}} + \frac{2n({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)}))ln(x)}{x^{3}} + \frac{2n{x}^{n}}{x^{3}(x)} - \frac{3n^{2}*-3{x}^{n}ln(x)}{x^{4}} - \frac{3n^{2}({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)}))ln(x)}{x^{3}} - \frac{3n^{2}{x}^{n}}{x^{3}(x)} + \frac{n^{3}*-3{x}^{n}ln(x)}{x^{4}} + \frac{n^{3}({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)}))ln(x)}{x^{3}} + \frac{n^{3}{x}^{n}}{x^{3}(x)} - \frac{6n*-3{x}^{n}}{x^{4}} - \frac{6n({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)}))}{x^{3}} + \frac{3n^{2}*-3{x}^{n}}{x^{4}} + \frac{3n^{2}({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)}))}{x^{3}} + \frac{2*-3{x}^{n}}{x^{4}} + \frac{2({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)}))}{x^{3}}\\=&\frac{-6n{x}^{n}ln(x)}{x^{4}} + \frac{11n^{2}{x}^{n}ln(x)}{x^{4}} - \frac{6n^{3}{x}^{n}ln(x)}{x^{4}} + \frac{n^{4}{x}^{n}ln(x)}{x^{4}} + \frac{22n{x}^{n}}{x^{4}} - \frac{18n^{2}{x}^{n}}{x^{4}} + \frac{4n^{3}{x}^{n}}{x^{4}} - \frac{6{x}^{n}}{x^{4}}\\ \end{split}\end{equation} \]

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