There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sin(x)sin(2x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(x)sin(2x)\right)}{dx}\\=&cos(x)sin(2x) + sin(x)cos(2x)*2\\=&sin(2x)cos(x) + 2sin(x)cos(2x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( sin(2x)cos(x) + 2sin(x)cos(2x)\right)}{dx}\\=&cos(2x)*2cos(x) + sin(2x)*-sin(x) + 2cos(x)cos(2x) + 2sin(x)*-sin(2x)*2\\=&2cos(2x)cos(x) - sin(x)sin(2x) + 2cos(x)cos(2x) - 4sin(2x)sin(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2cos(2x)cos(x) - sin(x)sin(2x) + 2cos(x)cos(2x) - 4sin(2x)sin(x)\right)}{dx}\\=&2*-sin(2x)*2cos(x) + 2cos(2x)*-sin(x) - cos(x)sin(2x) - sin(x)cos(2x)*2 + 2*-sin(x)cos(2x) + 2cos(x)*-sin(2x)*2 - 4cos(2x)*2sin(x) - 4sin(2x)cos(x)\\=&-13sin(2x)cos(x) - 14sin(x)cos(2x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -13sin(2x)cos(x) - 14sin(x)cos(2x)\right)}{dx}\\=&-13cos(2x)*2cos(x) - 13sin(2x)*-sin(x) - 14cos(x)cos(2x) - 14sin(x)*-sin(2x)*2\\=&-26cos(2x)cos(x) + 13sin(x)sin(2x) - 14cos(x)cos(2x) + 28sin(2x)sin(x)\\ \end{split}\end{equation} \]

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