There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ -x{ln(x)}^{5} + 5x{ln(x)}^{4} - 19x{ln(x)}^{3} + 57x{ln(x)}^{2} - 114xln(x) + 114x\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -xln^{5}(x) + 5xln^{4}(x) - 19xln^{3}(x) + 57xln^{2}(x) - 114xln(x) + 114x\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -xln^{5}(x) + 5xln^{4}(x) - 19xln^{3}(x) + 57xln^{2}(x) - 114xln(x) + 114x\right)}{dx}\\=&-ln^{5}(x) - \frac{x*5ln^{4}(x)}{(x)} + 5ln^{4}(x) + \frac{5x*4ln^{3}(x)}{(x)} - 19ln^{3}(x) - \frac{19x*3ln^{2}(x)}{(x)} + 57ln^{2}(x) + \frac{57x*2ln(x)}{(x)} - 114ln(x) - \frac{114x}{(x)} + 114\\=&-ln^{5}(x) + ln^{3}(x)\\ \end{split}\end{equation} \]

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