There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ln(x)*2x - tan(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2xln(x) - tan(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2xln(x) - tan(x)\right)}{dx}\\=&2ln(x) + \frac{2x}{(x)} - sec^{2}(x)(1)\\=&2ln(x) - sec^{2}(x) + 2\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2ln(x) - sec^{2}(x) + 2\right)}{dx}\\=&\frac{2}{(x)} - 2sec^{2}(x)tan(x) + 0\\=&\frac{2}{x} - 2tan(x)sec^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2}{x} - 2tan(x)sec^{2}(x)\right)}{dx}\\=&\frac{2*-1}{x^{2}} - 2sec^{2}(x)(1)sec^{2}(x) - 2tan(x)*2sec^{2}(x)tan(x)\\=&\frac{-2}{x^{2}} - 2sec^{4}(x) - 4tan^{2}(x)sec^{2}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2}{x^{2}} - 2sec^{4}(x) - 4tan^{2}(x)sec^{2}(x)\right)}{dx}\\=&\frac{-2*-2}{x^{3}} - 2*4sec^{4}(x)tan(x) - 4*2tan(x)sec^{2}(x)(1)sec^{2}(x) - 4tan^{2}(x)*2sec^{2}(x)tan(x)\\=&\frac{4}{x^{3}} - 16tan(x)sec^{4}(x) - 8tan^{3}(x)sec^{2}(x)\\ \end{split}\end{equation} \]

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