- #1
hadroneater
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Homework Statement
f(x) = e^(x^2) * sin(x)
Find the value of the 3rd derivative at x = 0.
Homework 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)
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?