There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {sin(x)}^{20}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin^{20}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin^{20}(x)\right)}{dx}\\=&20sin^{19}(x)cos(x)\\=&20sin^{19}(x)cos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 20sin^{19}(x)cos(x)\right)}{dx}\\=&20*19sin^{18}(x)cos(x)cos(x) + 20sin^{19}(x)*-sin(x)\\=&380sin^{18}(x)cos^{2}(x) - 20sin^{20}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 380sin^{18}(x)cos^{2}(x) - 20sin^{20}(x)\right)}{dx}\\=&380*18sin^{17}(x)cos(x)cos^{2}(x) + 380sin^{18}(x)*-2cos(x)sin(x) - 20*20sin^{19}(x)cos(x)\\=&6840sin^{17}(x)cos^{3}(x) - 1160sin^{19}(x)cos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 6840sin^{17}(x)cos^{3}(x) - 1160sin^{19}(x)cos(x)\right)}{dx}\\=&6840*17sin^{16}(x)cos(x)cos^{3}(x) + 6840sin^{17}(x)*-3cos^{2}(x)sin(x) - 1160*19sin^{18}(x)cos(x)cos(x) - 1160sin^{19}(x)*-sin(x)\\=&116280sin^{16}(x)cos^{4}(x) - 42560sin^{18}(x)cos^{2}(x) + 1160sin^{20}(x)\\ \end{split}\end{equation} \]

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