How do i find the Maclaurin series?

Question

Use a known result (from the power series table) to find the Maclaurin series for f(x) = e^(3x).

Answer 1

Since it is the 4th degree then you need the 1st 4 terms of the e^x series to get
1 + x + x^2/2! + x^3/3! +x^4/4!

Plug in 3x for every x and simplify
1 + 3x + 9/2 x^2 + 27/6 x^3 + 81/24x^4