There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ln({x}^{cos({x}^{2})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln({x}^{cos(x^{2})})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln({x}^{cos(x^{2})})\right)}{dx}\\=&\frac{({x}^{cos(x^{2})}((-sin(x^{2})*2x)ln(x) + \frac{(cos(x^{2}))(1)}{(x)}))}{({x}^{cos(x^{2})})}\\=&-2xln(x)sin(x^{2}) + \frac{cos(x^{2})}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -2xln(x)sin(x^{2}) + \frac{cos(x^{2})}{x}\right)}{dx}\\=&-2ln(x)sin(x^{2}) - \frac{2xsin(x^{2})}{(x)} - 2xln(x)cos(x^{2})*2x + \frac{-cos(x^{2})}{x^{2}} + \frac{-sin(x^{2})*2x}{x}\\=&-2ln(x)sin(x^{2}) - 4sin(x^{2}) - 4x^{2}ln(x)cos(x^{2}) - \frac{cos(x^{2})}{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -2ln(x)sin(x^{2}) - 4sin(x^{2}) - 4x^{2}ln(x)cos(x^{2}) - \frac{cos(x^{2})}{x^{2}}\right)}{dx}\\=&\frac{-2sin(x^{2})}{(x)} - 2ln(x)cos(x^{2})*2x - 4cos(x^{2})*2x - 4*2xln(x)cos(x^{2}) - \frac{4x^{2}cos(x^{2})}{(x)} - 4x^{2}ln(x)*-sin(x^{2})*2x - \frac{-2cos(x^{2})}{x^{3}} - \frac{-sin(x^{2})*2x}{x^{2}}\\=& - 12xln(x)cos(x^{2}) - 12xcos(x^{2}) + 8x^{3}ln(x)sin(x^{2}) + \frac{2cos(x^{2})}{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - 12xln(x)cos(x^{2}) - 12xcos(x^{2}) + 8x^{3}ln(x)sin(x^{2}) + \frac{2cos(x^{2})}{x^{3}}\right)}{dx}\\=& - 12ln(x)cos(x^{2}) - \frac{12xcos(x^{2})}{(x)} - 12xln(x)*-sin(x^{2})*2x - 12cos(x^{2}) - 12x*-sin(x^{2})*2x + 8*3x^{2}ln(x)sin(x^{2}) + \frac{8x^{3}sin(x^{2})}{(x)} + 8x^{3}ln(x)cos(x^{2})*2x + \frac{2*-3cos(x^{2})}{x^{4}} + \frac{2*-sin(x^{2})*2x}{x^{3}}\\=& - 12ln(x)cos(x^{2}) - 24cos(x^{2}) + 48x^{2}ln(x)sin(x^{2}) + 32x^{2}sin(x^{2}) + 16x^{4}ln(x)cos(x^{2}) - \frac{6cos(x^{2})}{x^{4}} - \frac{4sin(x^{2})}{x^{2}}\\ \end{split}\end{equation} \]

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