There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {cos(x)}^{(\frac{13}{46})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {cos(x)}^{\frac{13}{46}}\right)}{dx}\\=&({cos(x)}^{\frac{13}{46}}((0)ln(cos(x)) + \frac{(\frac{13}{46})(-sin(x))}{(cos(x))}))\\=&\frac{-13sin(x)}{46cos^{\frac{33}{46}}(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-13sin(x)}{46cos^{\frac{33}{46}}(x)}\right)}{dx}\\=&\frac{-13cos(x)}{46cos^{\frac{33}{46}}(x)} - \frac{13sin(x)*\frac{33}{46}sin(x)}{46cos^{\frac{79}{46}}(x)}\\=&\frac{-13cos^{\frac{13}{46}}(x)}{46} - \frac{429sin^{2}(x)}{2116cos^{\frac{79}{46}}(x)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-13cos^{\frac{13}{46}}(x)}{46} - \frac{429sin^{2}(x)}{2116cos^{\frac{79}{46}}(x)}\right)}{dx}\\=&\frac{-13*\frac{-13}{46}sin(x)}{46cos^{\frac{33}{46}}(x)} - \frac{429*2sin(x)cos(x)}{2116cos^{\frac{79}{46}}(x)} - \frac{429sin^{2}(x)*\frac{79}{46}sin(x)}{2116cos^{\frac{125}{46}}(x)}\\=& - \frac{689sin(x)}{2116cos^{\frac{33}{46}}(x)} - \frac{33891sin^{3}(x)}{97336cos^{\frac{125}{46}}(x)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - \frac{689sin(x)}{2116cos^{\frac{33}{46}}(x)} - \frac{33891sin^{3}(x)}{97336cos^{\frac{125}{46}}(x)}\right)}{dx}\\=& - \frac{689cos(x)}{2116cos^{\frac{33}{46}}(x)} - \frac{689sin(x)*\frac{33}{46}sin(x)}{2116cos^{\frac{79}{46}}(x)} - \frac{33891*3sin^{2}(x)cos(x)}{97336cos^{\frac{125}{46}}(x)} - \frac{33891sin^{3}(x)*\frac{125}{46}sin(x)}{97336cos^{\frac{171}{46}}(x)}\\=& - \frac{689cos^{\frac{13}{46}}(x)}{2116} - \frac{62205sin^{2}(x)}{48668cos^{\frac{79}{46}}(x)} - \frac{4236375sin^{4}(x)}{4477456cos^{\frac{171}{46}}(x)}\\ \end{split}\end{equation} \]

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