What would be the easiest way I would be able to find the Taylor series of $$f(x) = (3x^2 + 2x -7)e^{5x}$$
I was reading I have to find the first few derivatives but I am not sure how helpful that is with this function. I was thinking of also using the fact that the Taylor series of $$e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}$$ but i am not sure how to. Any advice?
Writing the Taylor series for $e^{5x}$ and multiply it by $3x^2+2x-7$ is the easiest way. To find the Taylor series for $e^{5x}$ write the series for $e^x$ and replace $x$ with $5x$.