There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(({e}^{(6x)}sin(x))(\frac{1}{2}))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(\frac{1}{2}{e}^{(6x)}sin(x))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(\frac{1}{2}{e}^{(6x)}sin(x))\right)}{dx}\\=&\frac{(\frac{1}{2}({e}^{(6x)}((6)ln(e) + \frac{(6x)(0)}{(e)}))sin(x) + \frac{1}{2}{e}^{(6x)}cos(x))}{(\frac{1}{2}{e}^{(6x)}sin(x))}\\=&\frac{cos(x)}{sin(x)} + 6\\ \end{split}\end{equation} \]

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