There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ -ln(cos(x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -ln(cos(x))\right)}{dx}\\=&\frac{--sin(x)}{(cos(x))}\\=&\frac{sin(x)}{cos(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{sin(x)}{cos(x)}\right)}{dx}\\=&\frac{cos(x)}{cos(x)} + \frac{sin(x)sin(x)}{cos^{2}(x)}\\=&\frac{sin^{2}(x)}{cos^{2}(x)} + 1\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{sin^{2}(x)}{cos^{2}(x)} + 1\right)}{dx}\\=&\frac{2sin(x)cos(x)}{cos^{2}(x)} + \frac{sin^{2}(x)*2sin(x)}{cos^{3}(x)} + 0\\=&\frac{2sin(x)}{cos(x)} + \frac{2sin^{3}(x)}{cos^{3}(x)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2sin(x)}{cos(x)} + \frac{2sin^{3}(x)}{cos^{3}(x)}\right)}{dx}\\=&\frac{2cos(x)}{cos(x)} + \frac{2sin(x)sin(x)}{cos^{2}(x)} + \frac{2*3sin^{2}(x)cos(x)}{cos^{3}(x)} + \frac{2sin^{3}(x)*3sin(x)}{cos^{4}(x)}\\=&\frac{8sin^{2}(x)}{cos^{2}(x)} + \frac{6sin^{4}(x)}{cos^{4}(x)} + 2\\ \end{split}\end{equation} \]

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