There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{(xX + yY)}{(sqrt(xx + yy)sqrt(XX + YY))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{Xx}{sqrt(x^{2} + y^{2})sqrt(X^{2} + Y^{2})} + \frac{yY}{sqrt(x^{2} + y^{2})sqrt(X^{2} + Y^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{Xx}{sqrt(x^{2} + y^{2})sqrt(X^{2} + Y^{2})} + \frac{yY}{sqrt(x^{2} + y^{2})sqrt(X^{2} + Y^{2})}\right)}{dx}\\=&\frac{X}{sqrt(x^{2} + y^{2})sqrt(X^{2} + Y^{2})} + \frac{Xx*-(2x + 0)*\frac{1}{2}}{(x^{2} + y^{2})(x^{2} + y^{2})^{\frac{1}{2}}sqrt(X^{2} + Y^{2})} + \frac{Xx*-(0 + 0)*\frac{1}{2}}{sqrt(x^{2} + y^{2})(X^{2} + Y^{2})(X^{2} + Y^{2})^{\frac{1}{2}}} + \frac{yY*-(2x + 0)*\frac{1}{2}}{(x^{2} + y^{2})(x^{2} + y^{2})^{\frac{1}{2}}sqrt(X^{2} + Y^{2})} + \frac{yY*-(0 + 0)*\frac{1}{2}}{sqrt(x^{2} + y^{2})(X^{2} + Y^{2})(X^{2} + Y^{2})^{\frac{1}{2}}}\\=&\frac{X}{sqrt(x^{2} + y^{2})sqrt(X^{2} + Y^{2})} - \frac{Xx^{2}}{(x^{2} + y^{2})^{\frac{3}{2}}sqrt(X^{2} + Y^{2})} - \frac{yYx}{(x^{2} + y^{2})^{\frac{3}{2}}sqrt(X^{2} + Y^{2})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{X}{sqrt(x^{2} + y^{2})sqrt(X^{2} + Y^{2})} - \frac{Xx^{2}}{(x^{2} + y^{2})^{\frac{3}{2}}sqrt(X^{2} + Y^{2})} - \frac{yYx}{(x^{2} + y^{2})^{\frac{3}{2}}sqrt(X^{2} + Y^{2})}\right)}{dx}\\=&\frac{X*-(2x + 0)*\frac{1}{2}}{(x^{2} + y^{2})(x^{2} + y^{2})^{\frac{1}{2}}sqrt(X^{2} + Y^{2})} + \frac{X*-(0 + 0)*\frac{1}{2}}{sqrt(x^{2} + y^{2})(X^{2} + Y^{2})(X^{2} + Y^{2})^{\frac{1}{2}}} - \frac{(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + y^{2})^{\frac{5}{2}}})Xx^{2}}{sqrt(X^{2} + Y^{2})} - \frac{X*2x}{(x^{2} + y^{2})^{\frac{3}{2}}sqrt(X^{2} + Y^{2})} - \frac{Xx^{2}*-(0 + 0)*\frac{1}{2}}{(x^{2} + y^{2})^{\frac{3}{2}}(X^{2} + Y^{2})(X^{2} + Y^{2})^{\frac{1}{2}}} - \frac{(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + y^{2})^{\frac{5}{2}}})yYx}{sqrt(X^{2} + Y^{2})} - \frac{yY}{(x^{2} + y^{2})^{\frac{3}{2}}sqrt(X^{2} + Y^{2})} - \frac{yYx*-(0 + 0)*\frac{1}{2}}{(x^{2} + y^{2})^{\frac{3}{2}}(X^{2} + Y^{2})(X^{2} + Y^{2})^{\frac{1}{2}}}\\=&\frac{-3Xx}{(x^{2} + y^{2})^{\frac{3}{2}}sqrt(X^{2} + Y^{2})} + \frac{3Xx^{3}}{(x^{2} + y^{2})^{\frac{5}{2}}sqrt(X^{2} + Y^{2})} + \frac{3yYx^{2}}{(x^{2} + y^{2})^{\frac{5}{2}}sqrt(X^{2} + Y^{2})} - \frac{yY}{(x^{2} + y^{2})^{\frac{3}{2}}sqrt(X^{2} + Y^{2})}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3Xx}{(x^{2} + y^{2})^{\frac{3}{2}}sqrt(X^{2} + Y^{2})} + \frac{3Xx^{3}}{(x^{2} + y^{2})^{\frac{5}{2}}sqrt(X^{2} + Y^{2})} + \frac{3yYx^{2}}{(x^{2} + y^{2})^{\frac{5}{2}}sqrt(X^{2} + Y^{2})} - \frac{yY}{(x^{2} + y^{2})^{\frac{3}{2}}sqrt(X^{2} + Y^{2})}\right)}{dx}\\=&\frac{-3(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + y^{2})^{\frac{5}{2}}})Xx}{sqrt(X^{2} + Y^{2})} - \frac{3X}{(x^{2} + y^{2})^{\frac{3}{2}}sqrt(X^{2} + Y^{2})} - \frac{3Xx*-(0 + 0)*\frac{1}{2}}{(x^{2} + y^{2})^{\frac{3}{2}}(X^{2} + Y^{2})(X^{2} + Y^{2})^{\frac{1}{2}}} + \frac{3(\frac{\frac{-5}{2}(2x + 0)}{(x^{2} + y^{2})^{\frac{7}{2}}})Xx^{3}}{sqrt(X^{2} + Y^{2})} + \frac{3X*3x^{2}}{(x^{2} + y^{2})^{\frac{5}{2}}sqrt(X^{2} + Y^{2})} + \frac{3Xx^{3}*-(0 + 0)*\frac{1}{2}}{(x^{2} + y^{2})^{\frac{5}{2}}(X^{2} + Y^{2})(X^{2} + Y^{2})^{\frac{1}{2}}} + \frac{3(\frac{\frac{-5}{2}(2x + 0)}{(x^{2} + y^{2})^{\frac{7}{2}}})yYx^{2}}{sqrt(X^{2} + Y^{2})} + \frac{3yY*2x}{(x^{2} + y^{2})^{\frac{5}{2}}sqrt(X^{2} + Y^{2})} + \frac{3yYx^{2}*-(0 + 0)*\frac{1}{2}}{(x^{2} + y^{2})^{\frac{5}{2}}(X^{2} + Y^{2})(X^{2} + Y^{2})^{\frac{1}{2}}} - \frac{(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + y^{2})^{\frac{5}{2}}})yY}{sqrt(X^{2} + Y^{2})} - \frac{yY*-(0 + 0)*\frac{1}{2}}{(x^{2} + y^{2})^{\frac{3}{2}}(X^{2} + Y^{2})(X^{2} + Y^{2})^{\frac{1}{2}}}\\=&\frac{18Xx^{2}}{(x^{2} + y^{2})^{\frac{5}{2}}sqrt(X^{2} + Y^{2})} - \frac{3X}{(x^{2} + y^{2})^{\frac{3}{2}}sqrt(X^{2} + Y^{2})} - \frac{15Xx^{4}}{(x^{2} + y^{2})^{\frac{7}{2}}sqrt(X^{2} + Y^{2})} - \frac{15yYx^{3}}{(x^{2} + y^{2})^{\frac{7}{2}}sqrt(X^{2} + Y^{2})} + \frac{9yYx}{(x^{2} + y^{2})^{\frac{5}{2}}sqrt(X^{2} + Y^{2})}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{18Xx^{2}}{(x^{2} + y^{2})^{\frac{5}{2}}sqrt(X^{2} + Y^{2})} - \frac{3X}{(x^{2} + y^{2})^{\frac{3}{2}}sqrt(X^{2} + Y^{2})} - \frac{15Xx^{4}}{(x^{2} + y^{2})^{\frac{7}{2}}sqrt(X^{2} + Y^{2})} - \frac{15yYx^{3}}{(x^{2} + y^{2})^{\frac{7}{2}}sqrt(X^{2} + Y^{2})} + \frac{9yYx}{(x^{2} + y^{2})^{\frac{5}{2}}sqrt(X^{2} + Y^{2})}\right)}{dx}\\=&\frac{18(\frac{\frac{-5}{2}(2x + 0)}{(x^{2} + y^{2})^{\frac{7}{2}}})Xx^{2}}{sqrt(X^{2} + Y^{2})} + \frac{18X*2x}{(x^{2} + y^{2})^{\frac{5}{2}}sqrt(X^{2} + Y^{2})} + \frac{18Xx^{2}*-(0 + 0)*\frac{1}{2}}{(x^{2} + y^{2})^{\frac{5}{2}}(X^{2} + Y^{2})(X^{2} + Y^{2})^{\frac{1}{2}}} - \frac{3(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + y^{2})^{\frac{5}{2}}})X}{sqrt(X^{2} + Y^{2})} - \frac{3X*-(0 + 0)*\frac{1}{2}}{(x^{2} + y^{2})^{\frac{3}{2}}(X^{2} + Y^{2})(X^{2} + Y^{2})^{\frac{1}{2}}} - \frac{15(\frac{\frac{-7}{2}(2x + 0)}{(x^{2} + y^{2})^{\frac{9}{2}}})Xx^{4}}{sqrt(X^{2} + Y^{2})} - \frac{15X*4x^{3}}{(x^{2} + y^{2})^{\frac{7}{2}}sqrt(X^{2} + Y^{2})} - \frac{15Xx^{4}*-(0 + 0)*\frac{1}{2}}{(x^{2} + y^{2})^{\frac{7}{2}}(X^{2} + Y^{2})(X^{2} + Y^{2})^{\frac{1}{2}}} - \frac{15(\frac{\frac{-7}{2}(2x + 0)}{(x^{2} + y^{2})^{\frac{9}{2}}})yYx^{3}}{sqrt(X^{2} + Y^{2})} - \frac{15yY*3x^{2}}{(x^{2} + y^{2})^{\frac{7}{2}}sqrt(X^{2} + Y^{2})} - \frac{15yYx^{3}*-(0 + 0)*\frac{1}{2}}{(x^{2} + y^{2})^{\frac{7}{2}}(X^{2} + Y^{2})(X^{2} + Y^{2})^{\frac{1}{2}}} + \frac{9(\frac{\frac{-5}{2}(2x + 0)}{(x^{2} + y^{2})^{\frac{7}{2}}})yYx}{sqrt(X^{2} + Y^{2})} + \frac{9yY}{(x^{2} + y^{2})^{\frac{5}{2}}sqrt(X^{2} + Y^{2})} + \frac{9yYx*-(0 + 0)*\frac{1}{2}}{(x^{2} + y^{2})^{\frac{5}{2}}(X^{2} + Y^{2})(X^{2} + Y^{2})^{\frac{1}{2}}}\\=&\frac{-150Xx^{3}}{(x^{2} + y^{2})^{\frac{7}{2}}sqrt(X^{2} + Y^{2})} + \frac{45Xx}{(x^{2} + y^{2})^{\frac{5}{2}}sqrt(X^{2} + Y^{2})} + \frac{105Xx^{5}}{(x^{2} + y^{2})^{\frac{9}{2}}sqrt(X^{2} + Y^{2})} + \frac{105yYx^{4}}{(x^{2} + y^{2})^{\frac{9}{2}}sqrt(X^{2} + Y^{2})} - \frac{90yYx^{2}}{(x^{2} + y^{2})^{\frac{7}{2}}sqrt(X^{2} + Y^{2})} + \frac{9yY}{(x^{2} + y^{2})^{\frac{5}{2}}sqrt(X^{2} + Y^{2})}\\ \end{split}\end{equation} \]

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