Differentiation, Second Derivative, of Functions Problem

[Loppyfoot]

Homework Statement

Suppose f(3)=2 , f'(3)=5 , and f''(3)= -2 . Then d²/dx² (f²(x)) at x=3 is equal to ____?

A. -20
B. 20
C. 38
D. 42
E. 10

The Attempt at a Solution

I am confused about how to find the function to get the derivative from that function. Any Ideas? Thanks.

 

[foxjwill]

You have two choices here: the chain rule and product rule.

 

[Loppyfoot]

So would the derive of f²(x)= 2f'(x) *1?

 

[Loppyfoot]

would that be the correct derivative?

 

[foxjwill]

would that be the correct derivative?

Nope. Remember that the chain rule gives that [f(g(x))]' = f'(g(x)) g'(x).