Question

Find the coefficient of x^3 in the Taylor series for e^3x about x=0.

Answer 1

each term is going to be something like
f^(n) ( 0 ) (x - 0)^n / n!
So we know we want n = 3 in order to get (x-0)^3 = x^3
We need to find f^(3) ( 0 ) / 3! since it is the coefficient.

Answer 2

where f^(3) is third derivative