There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{sqrt(xx)}{sqrt(xx + X)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{sqrt(x^{2})}{sqrt(x^{2} + X)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{sqrt(x^{2})}{sqrt(x^{2} + X)}\right)}{dx}\\=&\frac{2x*\frac{1}{2}}{(x^{2})^{\frac{1}{2}}sqrt(x^{2} + X)} + \frac{sqrt(x^{2})*-(2x + 0)*\frac{1}{2}}{(x^{2} + X)(x^{2} + X)^{\frac{1}{2}}}\\=&\frac{1}{sqrt(x^{2} + X)} - \frac{xsqrt(x^{2})}{(x^{2} + X)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{sqrt(x^{2} + X)} - \frac{xsqrt(x^{2})}{(x^{2} + X)^{\frac{3}{2}}}\right)}{dx}\\=&\frac{-(2x + 0)*\frac{1}{2}}{(x^{2} + X)(x^{2} + X)^{\frac{1}{2}}} - (\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + X)^{\frac{5}{2}}})xsqrt(x^{2}) - \frac{sqrt(x^{2})}{(x^{2} + X)^{\frac{3}{2}}} - \frac{x*2x*\frac{1}{2}}{(x^{2} + X)^{\frac{3}{2}}(x^{2})^{\frac{1}{2}}}\\=&\frac{3x^{2}sqrt(x^{2})}{(x^{2} + X)^{\frac{5}{2}}} - \frac{2x}{(x^{2} + X)^{\frac{3}{2}}} - \frac{sqrt(x^{2})}{(x^{2} + X)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{3x^{2}sqrt(x^{2})}{(x^{2} + X)^{\frac{5}{2}}} - \frac{2x}{(x^{2} + X)^{\frac{3}{2}}} - \frac{sqrt(x^{2})}{(x^{2} + X)^{\frac{3}{2}}}\right)}{dx}\\=&3(\frac{\frac{-5}{2}(2x + 0)}{(x^{2} + X)^{\frac{7}{2}}})x^{2}sqrt(x^{2}) + \frac{3*2xsqrt(x^{2})}{(x^{2} + X)^{\frac{5}{2}}} + \frac{3x^{2}*2x*\frac{1}{2}}{(x^{2} + X)^{\frac{5}{2}}(x^{2})^{\frac{1}{2}}} - 2(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + X)^{\frac{5}{2}}})x - \frac{2}{(x^{2} + X)^{\frac{3}{2}}} - (\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + X)^{\frac{5}{2}}})sqrt(x^{2}) - \frac{2x*\frac{1}{2}}{(x^{2} + X)^{\frac{3}{2}}(x^{2})^{\frac{1}{2}}}\\=& - \frac{15x^{3}sqrt(x^{2})}{(x^{2} + X)^{\frac{7}{2}}} + \frac{9xsqrt(x^{2})}{(x^{2} + X)^{\frac{5}{2}}} + \frac{9x^{2}}{(x^{2} + X)^{\frac{5}{2}}} - \frac{3}{(x^{2} + X)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - \frac{15x^{3}sqrt(x^{2})}{(x^{2} + X)^{\frac{7}{2}}} + \frac{9xsqrt(x^{2})}{(x^{2} + X)^{\frac{5}{2}}} + \frac{9x^{2}}{(x^{2} + X)^{\frac{5}{2}}} - \frac{3}{(x^{2} + X)^{\frac{3}{2}}}\right)}{dx}\\=& - 15(\frac{\frac{-7}{2}(2x + 0)}{(x^{2} + X)^{\frac{9}{2}}})x^{3}sqrt(x^{2}) - \frac{15*3x^{2}sqrt(x^{2})}{(x^{2} + X)^{\frac{7}{2}}} - \frac{15x^{3}*2x*\frac{1}{2}}{(x^{2} + X)^{\frac{7}{2}}(x^{2})^{\frac{1}{2}}} + 9(\frac{\frac{-5}{2}(2x + 0)}{(x^{2} + X)^{\frac{7}{2}}})xsqrt(x^{2}) + \frac{9sqrt(x^{2})}{(x^{2} + X)^{\frac{5}{2}}} + \frac{9x*2x*\frac{1}{2}}{(x^{2} + X)^{\frac{5}{2}}(x^{2})^{\frac{1}{2}}} + 9(\frac{\frac{-5}{2}(2x + 0)}{(x^{2} + X)^{\frac{7}{2}}})x^{2} + \frac{9*2x}{(x^{2} + X)^{\frac{5}{2}}} - 3(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + X)^{\frac{5}{2}}})\\=&\frac{105x^{4}sqrt(x^{2})}{(x^{2} + X)^{\frac{9}{2}}} - \frac{90x^{2}sqrt(x^{2})}{(x^{2} + X)^{\frac{7}{2}}} - \frac{60x^{3}}{(x^{2} + X)^{\frac{7}{2}}} + \frac{9sqrt(x^{2})}{(x^{2} + X)^{\frac{5}{2}}} + \frac{36x}{(x^{2} + X)^{\frac{5}{2}}}\\ \end{split}\end{equation} \]

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