There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sin(x){\frac{1}{\frac{27}{10}}}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {\frac{10}{27}}^{x}sin(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {\frac{10}{27}}^{x}sin(x)\right)}{dx}\\=&({\frac{10}{27}}^{x}((1)ln(\frac{10}{27}) + \frac{(x)(0)}{(\frac{10}{27})}))sin(x) + {\frac{10}{27}}^{x}cos(x)\\=&{\frac{10}{27}}^{x}ln(\frac{10}{27})sin(x) + {\frac{10}{27}}^{x}cos(x)\\ \end{split}\end{equation} \]

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