1. The problem statement, all variables and given/known data f(x) = e^(x^2) * sin(x) Find the value of the 3rd derivative at x = 0. 2. Relevant equations e^x = 1 + x + x^2/2! + ... + x^n/n! sin(x) = 1 + x^3/3! - x^5/5! + ... + x^(2n+1)/(2n+1)! * (-1)^(n-1) 3. The attempt at a solution I know I should plug in the two series into f(x). But what is e^(x^2)? Would I have to basically square the power series of e^x? So let's just make n = 3, then f(x) = (1 + x + x^2/2! + x^3/3!)^2 * (1 + x^3/3! - x^5/5! + x^7/7!) Then the expression becomes extremely complex for me. Even if I manage to expand the whole thing, how would I use it to find the third derivative?