There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ cos(x)ln(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(x)cos(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(x)cos(x)\right)}{dx}\\=&\frac{cos(x)}{(x)} + ln(x)*-sin(x)\\=&\frac{cos(x)}{x} - ln(x)sin(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{cos(x)}{x} - ln(x)sin(x)\right)}{dx}\\=&\frac{-cos(x)}{x^{2}} + \frac{-sin(x)}{x} - \frac{sin(x)}{(x)} - ln(x)cos(x)\\=&\frac{-cos(x)}{x^{2}} - \frac{2sin(x)}{x} - ln(x)cos(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-cos(x)}{x^{2}} - \frac{2sin(x)}{x} - ln(x)cos(x)\right)}{dx}\\=&\frac{--2cos(x)}{x^{3}} - \frac{-sin(x)}{x^{2}} - \frac{2*-sin(x)}{x^{2}} - \frac{2cos(x)}{x} - \frac{cos(x)}{(x)} - ln(x)*-sin(x)\\=&\frac{2cos(x)}{x^{3}} + \frac{3sin(x)}{x^{2}} - \frac{3cos(x)}{x} + ln(x)sin(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2cos(x)}{x^{3}} + \frac{3sin(x)}{x^{2}} - \frac{3cos(x)}{x} + ln(x)sin(x)\right)}{dx}\\=&\frac{2*-3cos(x)}{x^{4}} + \frac{2*-sin(x)}{x^{3}} + \frac{3*-2sin(x)}{x^{3}} + \frac{3cos(x)}{x^{2}} - \frac{3*-cos(x)}{x^{2}} - \frac{3*-sin(x)}{x} + \frac{sin(x)}{(x)} + ln(x)cos(x)\\=&\frac{-6cos(x)}{x^{4}} - \frac{8sin(x)}{x^{3}} + \frac{6cos(x)}{x^{2}} + \frac{4sin(x)}{x} + ln(x)cos(x)\\ \end{split}\end{equation} \]

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