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

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