# Derivative Problem

• Aug 25th 2010, 11:23 PM
RU2010
Derivative Problem

Let g(x)=x^3 f(x). Compute g'(2) given that f(2) = 3 and f'(2) = -1.

Any help with this problem would be much appreciated...
• Aug 25th 2010, 11:29 PM
CaptainBlack
Quote:

Originally Posted by RU2010

Let g(x)=x^3 f(x). Compute g'(2) given that f(2) = 3 and f'(2) = -1.

Any help with this problem would be much appreciated...

Start by differentiating g(x) (use the product rule), if you are then still having problems ask again.

CB
• Aug 26th 2010, 08:09 PM
RU2010
Ok, I have differentiated g(x) = x^3 f(x) , which is g'(x) = 3x^2 f(x) + x^3 f'(x). Given that f(2) = 3 and f'(2) = -1, how do I find out what f(x) is? I'm stuck....
• Aug 26th 2010, 09:13 PM
Isomorphism
Quote:

Originally Posted by RU2010
Ok, I have differentiated g(x) = x^3 f(x) , which is g'(x) = 3x^2 f(x) + x^3 f'(x). Given that f(2) = 3 and f'(2) = -1, how do I find out what f(x) is? I'm stuck....

But the question just asks you to compute g'(2). Why do you need f(x)?

Quote:

Originally Posted by RU2010

Let g(x)=x^3 f(x). Compute g'(2) given that f(2) = 3 and f'(2) = -1.

Any help with this problem would be much appreciated...

• Aug 27th 2010, 04:43 AM
RU2010
f(x) is part of g(x), so I think I need to know what f(x) is in order to full differentiate g'(x). Since the problem gives the value of f(2)=3, and f'(2), I'm trying to use that information to find f(x). I'm still stuck.
• Aug 27th 2010, 04:53 AM
Defunkt
But as they said, you don't need to explicitly find f(x).
The derivative of g(x) is $g'(x) = 3x^2f(x) + x^3f'(x)$
You need to find $g'(2) = 3 \cdot 2^2 \cdot f(2) + 2^3 \cdot f'(2)$. You have f(2) and f'(2) - what more do you need?
• Aug 27th 2010, 05:02 AM
RU2010
Quote:

Originally Posted by Defunkt
But as they said, you don't need to explicitly find f(x).
The derivative of g(x) is $g'(x) = 3x^2f(x) + x^3f'(x)$
You need to find $g'(2) = 3 \cdot 2^2 \cdot f(2) + 2^3 \cdot f'(2)$. You have f(2) and f'(2) - what more do you need?

Ok, the light bulb just came on! I see the answer now, and it was staring at me the entire time!

Thanks guys.