There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{1}{(1 + {x}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{(x^{2} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{(x^{2} + 1)}\right)}{dx}\\=&(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})\\=&\frac{-2x}{(x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2x}{(x^{2} + 1)^{2}}\right)}{dx}\\=&-2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x - \frac{2}{(x^{2} + 1)^{2}}\\=&\frac{8x^{2}}{(x^{2} + 1)^{3}} - \frac{2}{(x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{8x^{2}}{(x^{2} + 1)^{3}} - \frac{2}{(x^{2} + 1)^{2}}\right)}{dx}\\=&8(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x^{2} + \frac{8*2x}{(x^{2} + 1)^{3}} - 2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})\\=&\frac{-48x^{3}}{(x^{2} + 1)^{4}} + \frac{24x}{(x^{2} + 1)^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-48x^{3}}{(x^{2} + 1)^{4}} + \frac{24x}{(x^{2} + 1)^{3}}\right)}{dx}\\=&-48(\frac{-4(2x + 0)}{(x^{2} + 1)^{5}})x^{3} - \frac{48*3x^{2}}{(x^{2} + 1)^{4}} + 24(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x + \frac{24}{(x^{2} + 1)^{3}}\\=&\frac{384x^{4}}{(x^{2} + 1)^{5}} - \frac{288x^{2}}{(x^{2} + 1)^{4}} + \frac{24}{(x^{2} + 1)^{3}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！