There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {cos(sqrt(x))}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = cos^{2}(sqrt(x))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( cos^{2}(sqrt(x))\right)}{dx}\\=&\frac{-2cos(sqrt(x))sin(sqrt(x))*\frac{1}{2}}{(x)^{\frac{1}{2}}}\\=&\frac{-sin(sqrt(x))cos(sqrt(x))}{x^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-sin(sqrt(x))cos(sqrt(x))}{x^{\frac{1}{2}}}\right)}{dx}\\=&\frac{-\frac{-1}{2}sin(sqrt(x))cos(sqrt(x))}{x^{\frac{3}{2}}} - \frac{cos(sqrt(x))*\frac{1}{2}cos(sqrt(x))}{x^{\frac{1}{2}}(x)^{\frac{1}{2}}} - \frac{sin(sqrt(x))*-sin(sqrt(x))*\frac{1}{2}}{x^{\frac{1}{2}}(x)^{\frac{1}{2}}}\\=&\frac{sin(sqrt(x))cos(sqrt(x))}{2x^{\frac{3}{2}}} - \frac{cos^{2}(sqrt(x))}{2x} + \frac{sin^{2}(sqrt(x))}{2x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{sin(sqrt(x))cos(sqrt(x))}{2x^{\frac{3}{2}}} - \frac{cos^{2}(sqrt(x))}{2x} + \frac{sin^{2}(sqrt(x))}{2x}\right)}{dx}\\=&\frac{\frac{-3}{2}sin(sqrt(x))cos(sqrt(x))}{2x^{\frac{5}{2}}} + \frac{cos(sqrt(x))*\frac{1}{2}cos(sqrt(x))}{2x^{\frac{3}{2}}(x)^{\frac{1}{2}}} + \frac{sin(sqrt(x))*-sin(sqrt(x))*\frac{1}{2}}{2x^{\frac{3}{2}}(x)^{\frac{1}{2}}} - \frac{-cos^{2}(sqrt(x))}{2x^{2}} - \frac{-2cos(sqrt(x))sin(sqrt(x))*\frac{1}{2}}{2x(x)^{\frac{1}{2}}} + \frac{-sin^{2}(sqrt(x))}{2x^{2}} + \frac{2sin(sqrt(x))cos(sqrt(x))*\frac{1}{2}}{2x(x)^{\frac{1}{2}}}\\=&\frac{-3sin(sqrt(x))cos(sqrt(x))}{4x^{\frac{5}{2}}} + \frac{3cos^{2}(sqrt(x))}{4x^{2}} + \frac{sin(sqrt(x))cos(sqrt(x))}{x^{\frac{3}{2}}} - \frac{3sin^{2}(sqrt(x))}{4x^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3sin(sqrt(x))cos(sqrt(x))}{4x^{\frac{5}{2}}} + \frac{3cos^{2}(sqrt(x))}{4x^{2}} + \frac{sin(sqrt(x))cos(sqrt(x))}{x^{\frac{3}{2}}} - \frac{3sin^{2}(sqrt(x))}{4x^{2}}\right)}{dx}\\=&\frac{-3*\frac{-5}{2}sin(sqrt(x))cos(sqrt(x))}{4x^{\frac{7}{2}}} - \frac{3cos(sqrt(x))*\frac{1}{2}cos(sqrt(x))}{4x^{\frac{5}{2}}(x)^{\frac{1}{2}}} - \frac{3sin(sqrt(x))*-sin(sqrt(x))*\frac{1}{2}}{4x^{\frac{5}{2}}(x)^{\frac{1}{2}}} + \frac{3*-2cos^{2}(sqrt(x))}{4x^{3}} + \frac{3*-2cos(sqrt(x))sin(sqrt(x))*\frac{1}{2}}{4x^{2}(x)^{\frac{1}{2}}} + \frac{\frac{-3}{2}sin(sqrt(x))cos(sqrt(x))}{x^{\frac{5}{2}}} + \frac{cos(sqrt(x))*\frac{1}{2}cos(sqrt(x))}{x^{\frac{3}{2}}(x)^{\frac{1}{2}}} + \frac{sin(sqrt(x))*-sin(sqrt(x))*\frac{1}{2}}{x^{\frac{3}{2}}(x)^{\frac{1}{2}}} - \frac{3*-2sin^{2}(sqrt(x))}{4x^{3}} - \frac{3*2sin(sqrt(x))cos(sqrt(x))*\frac{1}{2}}{4x^{2}(x)^{\frac{1}{2}}}\\=&\frac{15sin(sqrt(x))cos(sqrt(x))}{8x^{\frac{7}{2}}} - \frac{15cos^{2}(sqrt(x))}{8x^{3}} - \frac{3sin(sqrt(x))cos(sqrt(x))}{x^{\frac{5}{2}}} + \frac{15sin^{2}(sqrt(x))}{8x^{3}} + \frac{cos^{2}(sqrt(x))}{2x^{2}} - \frac{sin^{2}(sqrt(x))}{2x^{2}}\\ \end{split}\end{equation} \]

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