There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {ln({x}^{2021})}^{2022}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln^{2022}(x^{2021})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln^{2022}(x^{2021})\right)}{dx}\\=&\frac{2022ln^{2021}(x^{2021})*2021x^{2020}}{(x^{2021})}\\=&\frac{4086462ln^{2021}(x^{2021})}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{4086462ln^{2021}(x^{2021})}{x}\right)}{dx}\\=&\frac{4086462*-ln^{2021}(x^{2021})}{x^{2}} + \frac{4086462*2021ln^{2020}(x^{2021})*2021x^{2020}}{x(x^{2021})}\\=&\frac{-4086462ln^{2021}(x^{2021})}{x^{2}} + \frac{16690912937742ln^{2020}(x^{2021})}{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-4086462ln^{2021}(x^{2021})}{x^{2}} + \frac{16690912937742ln^{2020}(x^{2021})}{x^{2}}\right)}{dx}\\=&\frac{-4086462*-2ln^{2021}(x^{2021})}{x^{3}} - \frac{4086462*2021ln^{2020}(x^{2021})*2021x^{2020}}{x^{2}(x^{2021})} + \frac{16690912937742*-2ln^{2020}(x^{2021})}{x^{3}} + \frac{16690912937742*2020ln^{2019}(x^{2021})*2021x^{2020}}{x^{2}(x^{2021})}\\=&\frac{8172924ln^{2021}(x^{2021})}{x^{3}} - \frac{50072738813226ln^{2020}(x^{2021})}{x^{3}} - \frac{5647659499541510824ln^{2019}(x^{2021})}{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{8172924ln^{2021}(x^{2021})}{x^{3}} - \frac{50072738813226ln^{2020}(x^{2021})}{x^{3}} - \frac{5647659499541510824ln^{2019}(x^{2021})}{x^{3}}\right)}{dx}\\=&\frac{8172924*-3ln^{2021}(x^{2021})}{x^{4}} + \frac{8172924*2021ln^{2020}(x^{2021})*2021x^{2020}}{x^{3}(x^{2021})} - \frac{50072738813226*-3ln^{2020}(x^{2021})}{x^{4}} - \frac{50072738813226*2020ln^{2019}(x^{2021})*2021x^{2020}}{x^{3}(x^{2021})} - \frac{5647659499541510824*-3ln^{2019}(x^{2021})}{x^{4}} - \frac{5647659499541510824*2019ln^{2018}(x^{2021})*2021x^{2020}}{x^{3}(x^{2021})}\\=&\frac{-24518772ln^{2021}(x^{2021})}{x^{4}} + \frac{183600042315162ln^{2020}(x^{2021})}{x^{4}} - \frac{3007531150170038288ln^{2019}(x^{2021})}{x^{4}} + \frac{1540276418388858920ln^{2018}(x^{2021})}{x^{4}}\\ \end{split}\end{equation} \]

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