There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(tan(x))}^{100}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = tan^{100}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( tan^{100}(x)\right)}{dx}\\=&100tan^{99}(x)sec^{2}(x)(1)\\=&100tan^{99}(x)sec^{2}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 100tan^{99}(x)sec^{2}(x)\right)}{dx}\\=&100*99tan^{98}(x)sec^{2}(x)(1)sec^{2}(x) + 100tan^{99}(x)*2sec^{2}(x)tan(x)\\=&9900tan^{98}(x)sec^{4}(x) + 200tan^{100}(x)sec^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 9900tan^{98}(x)sec^{4}(x) + 200tan^{100}(x)sec^{2}(x)\right)}{dx}\\=&9900*98tan^{97}(x)sec^{2}(x)(1)sec^{4}(x) + 9900tan^{98}(x)*4sec^{4}(x)tan(x) + 200*100tan^{99}(x)sec^{2}(x)(1)sec^{2}(x) + 200tan^{100}(x)*2sec^{2}(x)tan(x)\\=&970200tan^{97}(x)sec^{6}(x) + 59600tan^{99}(x)sec^{4}(x) + 400tan^{101}(x)sec^{2}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 970200tan^{97}(x)sec^{6}(x) + 59600tan^{99}(x)sec^{4}(x) + 400tan^{101}(x)sec^{2}(x)\right)}{dx}\\=&970200*97tan^{96}(x)sec^{2}(x)(1)sec^{6}(x) + 970200tan^{97}(x)*6sec^{6}(x)tan(x) + 59600*99tan^{98}(x)sec^{2}(x)(1)sec^{4}(x) + 59600tan^{99}(x)*4sec^{4}(x)tan(x) + 400*101tan^{100}(x)sec^{2}(x)(1)sec^{2}(x) + 400tan^{101}(x)*2sec^{2}(x)tan(x)\\=&94109400tan^{96}(x)sec^{8}(x) + 11721600tan^{98}(x)sec^{6}(x) + 278800tan^{100}(x)sec^{4}(x) + 800tan^{102}(x)sec^{2}(x)\\ \end{split}\end{equation} \]

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