There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(sin(x))}^{4}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin^{4}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin^{4}(x)\right)}{dx}\\=&4sin^{3}(x)cos(x)\\=&4sin^{3}(x)cos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 4sin^{3}(x)cos(x)\right)}{dx}\\=&4*3sin^{2}(x)cos(x)cos(x) + 4sin^{3}(x)*-sin(x)\\=&12sin^{2}(x)cos^{2}(x) - 4sin^{4}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 12sin^{2}(x)cos^{2}(x) - 4sin^{4}(x)\right)}{dx}\\=&12*2sin(x)cos(x)cos^{2}(x) + 12sin^{2}(x)*-2cos(x)sin(x) - 4*4sin^{3}(x)cos(x)\\=&24sin(x)cos^{3}(x) - 40sin^{3}(x)cos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 24sin(x)cos^{3}(x) - 40sin^{3}(x)cos(x)\right)}{dx}\\=&24cos(x)cos^{3}(x) + 24sin(x)*-3cos^{2}(x)sin(x) - 40*3sin^{2}(x)cos(x)cos(x) - 40sin^{3}(x)*-sin(x)\\=&24cos^{4}(x) - 192sin^{2}(x)cos^{2}(x) + 40sin^{4}(x)\\ \end{split}\end{equation} \]

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