There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{-sin(x)}{(ln(10)cos(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-sin(x)}{ln(10)cos(x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-sin(x)}{ln(10)cos(x)}\right)}{dx}\\=&\frac{--0sin(x)}{ln^{2}(10)(10)cos(x)} - \frac{cos(x)}{ln(10)cos(x)} - \frac{sin(x)sin(x)}{ln(10)cos^{2}(x)}\\=& - \frac{sin^{2}(x)}{ln(10)cos^{2}(x)} - \frac{1}{ln(10)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{sin^{2}(x)}{ln(10)cos^{2}(x)} - \frac{1}{ln(10)}\right)}{dx}\\=& - \frac{-0sin^{2}(x)}{ln^{2}(10)(10)cos^{2}(x)} - \frac{2sin(x)cos(x)}{ln(10)cos^{2}(x)} - \frac{sin^{2}(x)*2sin(x)}{ln(10)cos^{3}(x)} - \frac{-0}{ln^{2}(10)(10)}\\=& - \frac{2sin(x)}{ln(10)cos(x)} - \frac{2sin^{3}(x)}{ln(10)cos^{3}(x)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - \frac{2sin(x)}{ln(10)cos(x)} - \frac{2sin^{3}(x)}{ln(10)cos^{3}(x)}\right)}{dx}\\=& - \frac{2*-0sin(x)}{ln^{2}(10)(10)cos(x)} - \frac{2cos(x)}{ln(10)cos(x)} - \frac{2sin(x)sin(x)}{ln(10)cos^{2}(x)} - \frac{2*-0sin^{3}(x)}{ln^{2}(10)(10)cos^{3}(x)} - \frac{2*3sin^{2}(x)cos(x)}{ln(10)cos^{3}(x)} - \frac{2sin^{3}(x)*3sin(x)}{ln(10)cos^{4}(x)}\\=& - \frac{8sin^{2}(x)}{ln(10)cos^{2}(x)} - \frac{6sin^{4}(x)}{ln(10)cos^{4}(x)} - \frac{2}{ln(10)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - \frac{8sin^{2}(x)}{ln(10)cos^{2}(x)} - \frac{6sin^{4}(x)}{ln(10)cos^{4}(x)} - \frac{2}{ln(10)}\right)}{dx}\\=& - \frac{8*-0sin^{2}(x)}{ln^{2}(10)(10)cos^{2}(x)} - \frac{8*2sin(x)cos(x)}{ln(10)cos^{2}(x)} - \frac{8sin^{2}(x)*2sin(x)}{ln(10)cos^{3}(x)} - \frac{6*-0sin^{4}(x)}{ln^{2}(10)(10)cos^{4}(x)} - \frac{6*4sin^{3}(x)cos(x)}{ln(10)cos^{4}(x)} - \frac{6sin^{4}(x)*4sin(x)}{ln(10)cos^{5}(x)} - \frac{2*-0}{ln^{2}(10)(10)}\\=& - \frac{16sin(x)}{ln(10)cos(x)} - \frac{40sin^{3}(x)}{ln(10)cos^{3}(x)} - \frac{24sin^{5}(x)}{ln(10)cos^{5}(x)}\\ \end{split}\end{equation} \]

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