There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ({x}^{2} + 4x + 2){\frac{1}{\frac{27}{10}}}^{x}(2x + 2)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2x^{3}{\frac{10}{27}}^{x} + 10x^{2}{\frac{10}{27}}^{x} + 12x{\frac{10}{27}}^{x} + 4 * {\frac{10}{27}}^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2x^{3}{\frac{10}{27}}^{x} + 10x^{2}{\frac{10}{27}}^{x} + 12x{\frac{10}{27}}^{x} + 4 * {\frac{10}{27}}^{x}\right)}{dx}\\=&2*3x^{2}{\frac{10}{27}}^{x} + 2x^{3}({\frac{10}{27}}^{x}((1)ln(\frac{10}{27}) + \frac{(x)(0)}{(\frac{10}{27})})) + 10*2x{\frac{10}{27}}^{x} + 10x^{2}({\frac{10}{27}}^{x}((1)ln(\frac{10}{27}) + \frac{(x)(0)}{(\frac{10}{27})})) + 12 * {\frac{10}{27}}^{x} + 12x({\frac{10}{27}}^{x}((1)ln(\frac{10}{27}) + \frac{(x)(0)}{(\frac{10}{27})})) + 4({\frac{10}{27}}^{x}((1)ln(\frac{10}{27}) + \frac{(x)(0)}{(\frac{10}{27})}))\\=&2x^{3}{\frac{10}{27}}^{x}ln(\frac{10}{27}) + 10x^{2}{\frac{10}{27}}^{x}ln(\frac{10}{27}) + 12x{\frac{10}{27}}^{x}ln(\frac{10}{27}) + 6x^{2}{\frac{10}{27}}^{x} + 4 * {\frac{10}{27}}^{x}ln(\frac{10}{27}) + 20x{\frac{10}{27}}^{x} + 12 * {\frac{10}{27}}^{x}\\ \end{split}\end{equation} \]

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