What is the Quadratic Maclaurin Polynomial for f(x)=x*sin(x)?

[chief10]

Homework Statement

I'm having a bit of trouble with this Maclaurin Series question. It should be simple enough but I can't get the answer which is given as x². It's been a while since I've done series and my being rusty is a little annoying. Hopefully someone can help :) Consider:

f(x)=x*sin(x)

Question asks to find the Quadratic Maclaurin Polynomial for f(x).
So this is what I did. First I got the nth derivatives:

f¹(x) = x*cos(x) + sin(x)
f²(x) = -x*sin(x) + cos(x) + sin(x)

P₂(x): 0 + x*0 + (x^2)(0 + 1 + 0)*(1/2!)

= x²/2


I'm sure I'm doing something blatantly wrong here but I can't seem to work it out. Fresh eyes might be useful :)

Thanks a lot.

 

[chief10]

Oh no.. it was the derivative.. lol I've been racking my brain for 20 minutes staring at Taylor's Theorem thinking I made the error there.. ugh well that's embarrassing.