There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {sin(x)}^{100}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin^{100}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin^{100}(x)\right)}{dx}\\=&100sin^{99}(x)cos(x)\\=&100sin^{99}(x)cos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 100sin^{99}(x)cos(x)\right)}{dx}\\=&100*99sin^{98}(x)cos(x)cos(x) + 100sin^{99}(x)*-sin(x)\\=&9900sin^{98}(x)cos^{2}(x) - 100sin^{100}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 9900sin^{98}(x)cos^{2}(x) - 100sin^{100}(x)\right)}{dx}\\=&9900*98sin^{97}(x)cos(x)cos^{2}(x) + 9900sin^{98}(x)*-2cos(x)sin(x) - 100*100sin^{99}(x)cos(x)\\=&970200sin^{97}(x)cos^{3}(x) - 29800sin^{99}(x)cos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 970200sin^{97}(x)cos^{3}(x) - 29800sin^{99}(x)cos(x)\right)}{dx}\\=&970200*97sin^{96}(x)cos(x)cos^{3}(x) + 970200sin^{97}(x)*-3cos^{2}(x)sin(x) - 29800*99sin^{98}(x)cos(x)cos(x) - 29800sin^{99}(x)*-sin(x)\\=&94109400sin^{96}(x)cos^{4}(x) - 5860800sin^{98}(x)cos^{2}(x) + 29800sin^{100}(x)\\ \end{split}\end{equation} \]

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