There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sin(cos(ln(x*2)))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin(cos(ln(2x)))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(cos(ln(2x)))\right)}{dx}\\=&\frac{cos(cos(ln(2x)))*-sin(ln(2x))*2}{(2x)}\\=&\frac{-sin(ln(2x))cos(cos(ln(2x)))}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-sin(ln(2x))cos(cos(ln(2x)))}{x}\right)}{dx}\\=&\frac{--sin(ln(2x))cos(cos(ln(2x)))}{x^{2}} - \frac{cos(ln(2x))*2cos(cos(ln(2x)))}{x(2x)} - \frac{sin(ln(2x))*-sin(cos(ln(2x)))*-sin(ln(2x))*2}{x(2x)}\\=&\frac{sin(ln(2x))cos(cos(ln(2x)))}{x^{2}} - \frac{cos(ln(2x))cos(cos(ln(2x)))}{x^{2}} - \frac{sin(cos(ln(2x)))sin^{2}(ln(2x))}{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{sin(ln(2x))cos(cos(ln(2x)))}{x^{2}} - \frac{cos(ln(2x))cos(cos(ln(2x)))}{x^{2}} - \frac{sin(cos(ln(2x)))sin^{2}(ln(2x))}{x^{2}}\right)}{dx}\\=&\frac{-2sin(ln(2x))cos(cos(ln(2x)))}{x^{3}} + \frac{cos(ln(2x))*2cos(cos(ln(2x)))}{x^{2}(2x)} + \frac{sin(ln(2x))*-sin(cos(ln(2x)))*-sin(ln(2x))*2}{x^{2}(2x)} - \frac{-2cos(ln(2x))cos(cos(ln(2x)))}{x^{3}} - \frac{-sin(ln(2x))*2cos(cos(ln(2x)))}{x^{2}(2x)} - \frac{cos(ln(2x))*-sin(cos(ln(2x)))*-sin(ln(2x))*2}{x^{2}(2x)} - \frac{-2sin(cos(ln(2x)))sin^{2}(ln(2x))}{x^{3}} - \frac{cos(cos(ln(2x)))*-sin(ln(2x))*2sin^{2}(ln(2x))}{x^{2}(2x)} - \frac{sin(cos(ln(2x)))*2sin(ln(2x))cos(ln(2x))*2}{x^{2}(2x)}\\=&\frac{-sin(ln(2x))cos(cos(ln(2x)))}{x^{3}} + \frac{3cos(ln(2x))cos(cos(ln(2x)))}{x^{3}} - \frac{3sin(cos(ln(2x)))sin(ln(2x))cos(ln(2x))}{x^{3}} + \frac{3sin(cos(ln(2x)))sin^{2}(ln(2x))}{x^{3}} + \frac{sin^{3}(ln(2x))cos(cos(ln(2x)))}{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-sin(ln(2x))cos(cos(ln(2x)))}{x^{3}} + \frac{3cos(ln(2x))cos(cos(ln(2x)))}{x^{3}} - \frac{3sin(cos(ln(2x)))sin(ln(2x))cos(ln(2x))}{x^{3}} + \frac{3sin(cos(ln(2x)))sin^{2}(ln(2x))}{x^{3}} + \frac{sin^{3}(ln(2x))cos(cos(ln(2x)))}{x^{3}}\right)}{dx}\\=&\frac{--3sin(ln(2x))cos(cos(ln(2x)))}{x^{4}} - \frac{cos(ln(2x))*2cos(cos(ln(2x)))}{x^{3}(2x)} - \frac{sin(ln(2x))*-sin(cos(ln(2x)))*-sin(ln(2x))*2}{x^{3}(2x)} + \frac{3*-3cos(ln(2x))cos(cos(ln(2x)))}{x^{4}} + \frac{3*-sin(ln(2x))*2cos(cos(ln(2x)))}{x^{3}(2x)} + \frac{3cos(ln(2x))*-sin(cos(ln(2x)))*-sin(ln(2x))*2}{x^{3}(2x)} - \frac{3*-3sin(cos(ln(2x)))sin(ln(2x))cos(ln(2x))}{x^{4}} - \frac{3cos(cos(ln(2x)))*-sin(ln(2x))*2sin(ln(2x))cos(ln(2x))}{x^{3}(2x)} - \frac{3sin(cos(ln(2x)))cos(ln(2x))*2cos(ln(2x))}{x^{3}(2x)} - \frac{3sin(cos(ln(2x)))sin(ln(2x))*-sin(ln(2x))*2}{x^{3}(2x)} + \frac{3*-3sin(cos(ln(2x)))sin^{2}(ln(2x))}{x^{4}} + \frac{3cos(cos(ln(2x)))*-sin(ln(2x))*2sin^{2}(ln(2x))}{x^{3}(2x)} + \frac{3sin(cos(ln(2x)))*2sin(ln(2x))cos(ln(2x))*2}{x^{3}(2x)} + \frac{-3sin^{3}(ln(2x))cos(cos(ln(2x)))}{x^{4}} + \frac{3sin^{2}(ln(2x))cos(ln(2x))*2cos(cos(ln(2x)))}{x^{3}(2x)} + \frac{sin^{3}(ln(2x))*-sin(cos(ln(2x)))*-sin(ln(2x))*2}{x^{3}(2x)}\\=& - \frac{10cos(ln(2x))cos(cos(ln(2x)))}{x^{4}} + \frac{18sin(cos(ln(2x)))sin(ln(2x))cos(ln(2x))}{x^{4}} + \frac{3sin^{2}(ln(2x))cos(ln(2x))cos(cos(ln(2x)))}{x^{4}} - \frac{7sin(cos(ln(2x)))sin^{2}(ln(2x))}{x^{4}} + \frac{3sin^{2}(ln(2x))cos(cos(ln(2x)))cos(ln(2x))}{x^{4}} - \frac{3sin(cos(ln(2x)))cos^{2}(ln(2x))}{x^{4}} - \frac{6sin^{3}(ln(2x))cos(cos(ln(2x)))}{x^{4}} + \frac{sin(cos(ln(2x)))sin^{4}(ln(2x))}{x^{4}}\\ \end{split}\end{equation} \]

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