There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {cos(x)}^{(\frac{97}{266})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {cos(x)}^{\frac{97}{266}}\right)}{dx}\\=&({cos(x)}^{\frac{97}{266}}((0)ln(cos(x)) + \frac{(\frac{97}{266})(-sin(x))}{(cos(x))}))\\=&\frac{-97sin(x)}{266cos^{\frac{169}{266}}(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-97sin(x)}{266cos^{\frac{169}{266}}(x)}\right)}{dx}\\=&\frac{-97cos(x)}{266cos^{\frac{169}{266}}(x)} - \frac{97sin(x)*\frac{169}{266}sin(x)}{266cos^{\frac{435}{266}}(x)}\\=&\frac{-97cos^{\frac{97}{266}}(x)}{266} - \frac{16393sin^{2}(x)}{70756cos^{\frac{435}{266}}(x)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-97cos^{\frac{97}{266}}(x)}{266} - \frac{16393sin^{2}(x)}{70756cos^{\frac{435}{266}}(x)}\right)}{dx}\\=&\frac{-97*\frac{-97}{266}sin(x)}{266cos^{\frac{169}{266}}(x)} - \frac{16393*2sin(x)cos(x)}{70756cos^{\frac{435}{266}}(x)} - \frac{16393sin^{2}(x)*\frac{435}{266}sin(x)}{70756cos^{\frac{701}{266}}(x)}\\=& - \frac{23377sin(x)}{70756cos^{\frac{169}{266}}(x)} - \frac{7130955sin^{3}(x)}{18821096cos^{\frac{701}{266}}(x)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - \frac{23377sin(x)}{70756cos^{\frac{169}{266}}(x)} - \frac{7130955sin^{3}(x)}{18821096cos^{\frac{701}{266}}(x)}\right)}{dx}\\=& - \frac{23377cos(x)}{70756cos^{\frac{169}{266}}(x)} - \frac{23377sin(x)*\frac{169}{266}sin(x)}{70756cos^{\frac{435}{266}}(x)} - \frac{7130955*3sin^{2}(x)cos(x)}{18821096cos^{\frac{701}{266}}(x)} - \frac{7130955sin^{3}(x)*\frac{701}{266}sin(x)}{18821096cos^{\frac{967}{266}}(x)}\\=& - \frac{23377cos^{\frac{97}{266}}(x)}{70756} - \frac{12671789sin^{2}(x)}{9410548cos^{\frac{435}{266}}(x)} - \frac{4998799455sin^{4}(x)}{5006411536cos^{\frac{967}{266}}(x)}\\ \end{split}\end{equation} \]

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