There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {sin(x)}^{23456789}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin^{23456789}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin^{23456789}(x)\right)}{dx}\\=&23456789sin^{23456788}(x)cos(x)\\=&23456789sin^{23456788}(x)cos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 23456789sin^{23456788}(x)cos(x)\right)}{dx}\\=&23456789*23456788sin^{23456787}(x)cos(x)cos(x) + 23456789sin^{23456788}(x)*-sin(x)\\=&550220926733732sin^{23456787}(x)cos^{2}(x) - 23456789sin^{23456789}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 550220926733732sin^{23456787}(x)cos^{2}(x) - 23456789sin^{23456789}(x)\right)}{dx}\\=&550220926733732*23456787sin^{23456786}(x)cos(x)cos^{2}(x) + 550220926733732sin^{23456787}(x)*-2cos(x)sin(x) - 23456789*23456789sin^{23456788}(x)cos(x)\\=&-6305770260928892116sin^{23456786}(x)cos^{3}(x) - 1650662803657985sin^{23456788}(x)cos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -6305770260928892116sin^{23456786}(x)cos^{3}(x) - 1650662803657985sin^{23456788}(x)cos(x)\right)}{dx}\\=&-6305770260928892116*23456786sin^{23456785}(x)cos(x)cos^{3}(x) - 6305770260928892116sin^{23456786}(x)*-3cos^{2}(x)sin(x) - 1650662803657985*23456788sin^{23456787}(x)cos(x)cos(x) - 1650662803657985sin^{23456788}(x)*-sin(x)\\=&-7596301620547639016sin^{23456785}(x)cos^{4}(x) + 938932534447314536sin^{23456787}(x)cos^{2}(x) + 1650662803657985sin^{23456789}(x)\\ \end{split}\end{equation} \]

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