There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln({({e}^{(6x)}sin(x))}^{\frac{1}{2}})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln({e}^{(3x)}sin^{\frac{1}{2}}(x))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln({e}^{(3x)}sin^{\frac{1}{2}}(x))\right)}{dx}\\=&\frac{(({e}^{(3x)}((3)ln(e) + \frac{(3x)(0)}{(e)}))sin^{\frac{1}{2}}(x) + \frac{{e}^{(3x)}*\frac{1}{2}cos(x)}{sin^{\frac{1}{2}}(x)})}{({e}^{(3x)}sin^{\frac{1}{2}}(x))}\\=&\frac{cos(x)}{2sin(x)} + 3\\ \end{split}\end{equation} \]

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