There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(xln(x))}^{5}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{5}ln^{5}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{5}ln^{5}(x)\right)}{dx}\\=&5x^{4}ln^{5}(x) + \frac{x^{5}*5ln^{4}(x)}{(x)}\\=&5x^{4}ln^{5}(x) + 5x^{4}ln^{4}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 5x^{4}ln^{5}(x) + 5x^{4}ln^{4}(x)\right)}{dx}\\=&5*4x^{3}ln^{5}(x) + \frac{5x^{4}*5ln^{4}(x)}{(x)} + 5*4x^{3}ln^{4}(x) + \frac{5x^{4}*4ln^{3}(x)}{(x)}\\=&20x^{3}ln^{5}(x) + 45x^{3}ln^{4}(x) + 20x^{3}ln^{3}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 20x^{3}ln^{5}(x) + 45x^{3}ln^{4}(x) + 20x^{3}ln^{3}(x)\right)}{dx}\\=&20*3x^{2}ln^{5}(x) + \frac{20x^{3}*5ln^{4}(x)}{(x)} + 45*3x^{2}ln^{4}(x) + \frac{45x^{3}*4ln^{3}(x)}{(x)} + 20*3x^{2}ln^{3}(x) + \frac{20x^{3}*3ln^{2}(x)}{(x)}\\=&60x^{2}ln^{5}(x) + 235x^{2}ln^{4}(x) + 240x^{2}ln^{3}(x) + 60x^{2}ln^{2}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 60x^{2}ln^{5}(x) + 235x^{2}ln^{4}(x) + 240x^{2}ln^{3}(x) + 60x^{2}ln^{2}(x)\right)}{dx}\\=&60*2xln^{5}(x) + \frac{60x^{2}*5ln^{4}(x)}{(x)} + 235*2xln^{4}(x) + \frac{235x^{2}*4ln^{3}(x)}{(x)} + 240*2xln^{3}(x) + \frac{240x^{2}*3ln^{2}(x)}{(x)} + 60*2xln^{2}(x) + \frac{60x^{2}*2ln(x)}{(x)}\\=&120xln^{5}(x) + 770xln^{4}(x) + 1420xln^{3}(x) + 840xln^{2}(x) + 120xln(x)\\ \end{split}\end{equation} \]

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