There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {cos(x)}^{50}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = cos^{50}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( cos^{50}(x)\right)}{dx}\\=&-50cos^{49}(x)sin(x)\\=&-50sin(x)cos^{49}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -50sin(x)cos^{49}(x)\right)}{dx}\\=&-50cos(x)cos^{49}(x) - 50sin(x)*-49cos^{48}(x)sin(x)\\=&-50cos^{50}(x) + 2450sin^{2}(x)cos^{48}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -50cos^{50}(x) + 2450sin^{2}(x)cos^{48}(x)\right)}{dx}\\=&-50*-50cos^{49}(x)sin(x) + 2450*2sin(x)cos(x)cos^{48}(x) + 2450sin^{2}(x)*-48cos^{47}(x)sin(x)\\=&7400sin(x)cos^{49}(x) - 117600sin^{3}(x)cos^{47}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 7400sin(x)cos^{49}(x) - 117600sin^{3}(x)cos^{47}(x)\right)}{dx}\\=&7400cos(x)cos^{49}(x) + 7400sin(x)*-49cos^{48}(x)sin(x) - 117600*3sin^{2}(x)cos(x)cos^{47}(x) - 117600sin^{3}(x)*-47cos^{46}(x)sin(x)\\=&7400cos^{50}(x) - 715400sin^{2}(x)cos^{48}(x) + 5527200sin^{4}(x)cos^{46}(x)\\ \end{split}\end{equation} \]

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