There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(cos(3x + 1))}^{99999999}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = cos^{99999999}(3x + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( cos^{99999999}(3x + 1)\right)}{dx}\\=&-99999999cos^{99999998}(3x + 1)sin(3x + 1)(3 + 0)\\=&-299999997sin(3x + 1)cos^{99999998}(3x + 1)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -299999997sin(3x + 1)cos^{99999998}(3x + 1)\right)}{dx}\\=&-299999997cos(3x + 1)(3 + 0)cos^{99999998}(3x + 1) - 299999997sin(3x + 1)*-99999998cos^{99999997}(3x + 1)sin(3x + 1)(3 + 0)\\=&-899999991cos^{99999999}(3x + 1) + 89999997300000018sin^{2}(3x + 1)cos^{99999997}(3x + 1)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -899999991cos^{99999999}(3x + 1) + 89999997300000018sin^{2}(3x + 1)cos^{99999997}(3x + 1)\right)}{dx}\\=&-899999991*-99999999cos^{99999998}(3x + 1)sin(3x + 1)(3 + 0) + 89999997300000018*2sin(3x + 1)cos(3x + 1)(3 + 0)cos^{99999997}(3x + 1) + 89999997300000018sin^{2}(3x + 1)*-99999997cos^{99999996}(3x + 1)sin(3x + 1)(3 + 0)\\=&809999978400000135sin(3x + 1)cos^{99999998}(3x + 1) + 2858598650842445730sin^{3}(3x + 1)cos^{99999996}(3x + 1)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 809999978400000135sin(3x + 1)cos^{99999998}(3x + 1) + 2858598650842445730sin^{3}(3x + 1)cos^{99999996}(3x + 1)\right)}{dx}\\=&809999978400000135cos(3x + 1)(3 + 0)cos^{99999998}(3x + 1) + 809999978400000135sin(3x + 1)*-99999998cos^{99999997}(3x + 1)sin(3x + 1)(3 + 0) + 2858598650842445730*3sin^{2}(3x + 1)cos(3x + 1)(3 + 0)cos^{99999996}(3x + 1) + 2858598650842445730sin^{3}(3x + 1)*-99999996cos^{99999995}(3x + 1)sin(3x + 1)(3 + 0)\\=&2429999935200000405cos^{99999999}(3x + 1) - 7125456408764632356sin^{2}(3x + 1)cos^{99999997}(3x + 1) - 2822967109520099944sin^{4}(3x + 1)cos^{99999995}(3x + 1)\\ \end{split}\end{equation} \]

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