There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{{x}^{10}}{(1 - x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{10}}{(-x + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{10}}{(-x + 1)}\right)}{dx}\\=&(\frac{-(-1 + 0)}{(-x + 1)^{2}})x^{10} + \frac{10x^{9}}{(-x + 1)}\\=&\frac{x^{10}}{(-x + 1)^{2}} + \frac{10x^{9}}{(-x + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{x^{10}}{(-x + 1)^{2}} + \frac{10x^{9}}{(-x + 1)}\right)}{dx}\\=&(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x^{10} + \frac{10x^{9}}{(-x + 1)^{2}} + 10(\frac{-(-1 + 0)}{(-x + 1)^{2}})x^{9} + \frac{10*9x^{8}}{(-x + 1)}\\=&\frac{2x^{10}}{(-x + 1)^{3}} + \frac{20x^{9}}{(-x + 1)^{2}} + \frac{90x^{8}}{(-x + 1)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2x^{10}}{(-x + 1)^{3}} + \frac{20x^{9}}{(-x + 1)^{2}} + \frac{90x^{8}}{(-x + 1)}\right)}{dx}\\=&2(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x^{10} + \frac{2*10x^{9}}{(-x + 1)^{3}} + 20(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x^{9} + \frac{20*9x^{8}}{(-x + 1)^{2}} + 90(\frac{-(-1 + 0)}{(-x + 1)^{2}})x^{8} + \frac{90*8x^{7}}{(-x + 1)}\\=&\frac{6x^{10}}{(-x + 1)^{4}} + \frac{60x^{9}}{(-x + 1)^{3}} + \frac{270x^{8}}{(-x + 1)^{2}} + \frac{720x^{7}}{(-x + 1)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{6x^{10}}{(-x + 1)^{4}} + \frac{60x^{9}}{(-x + 1)^{3}} + \frac{270x^{8}}{(-x + 1)^{2}} + \frac{720x^{7}}{(-x + 1)}\right)}{dx}\\=&6(\frac{-4(-1 + 0)}{(-x + 1)^{5}})x^{10} + \frac{6*10x^{9}}{(-x + 1)^{4}} + 60(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x^{9} + \frac{60*9x^{8}}{(-x + 1)^{3}} + 270(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x^{8} + \frac{270*8x^{7}}{(-x + 1)^{2}} + 720(\frac{-(-1 + 0)}{(-x + 1)^{2}})x^{7} + \frac{720*7x^{6}}{(-x + 1)}\\=&\frac{24x^{10}}{(-x + 1)^{5}} + \frac{240x^{9}}{(-x + 1)^{4}} + \frac{1080x^{8}}{(-x + 1)^{3}} + \frac{2880x^{7}}{(-x + 1)^{2}} + \frac{5040x^{6}}{(-x + 1)}\\ \end{split}\end{equation} \]

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