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

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