How do I find the solution to this derivative problem?

[Cuisine123]

Homework Statement

Two functions f and g are such that f(4)=3, f prime (4)= -2, g(4)=7, and g prime (4)=5. Determine (1/g^2) prime(4). By "prime" I mean when there is something that looks like a little "1" exponent on the letter.

Please help and give clear step by step explanations. Thanks.

Homework Equations

N/A

The Attempt at a Solution

I know what is the quotient and product rules are, but I have no idea how to approach this question.

 

[n!kofeyn]

Have you learned the chain rule yet?

My hint is: what is the derivative of
$$\frac{1}{[g(x)]^2}?$$

 

[Cuisine123]

Have you learned the chain rule yet?

My hint is: what is the derivative of
$$\frac{1}{[g(x)]^2}?$$

Is it -2g(x)^-3 x g(x)?

 

[Oblakastouf]

Hint #2:
Chain rule: f(g(x)) = f'(g(x))g'(x)

In this case...
f(g(x)) = g(x)^-2

Soooo...

 

[n!kofeyn]

Is it -2g(x)^-3 x g(x)?

Exactly. Now evaluate your expression at x=4.

Also, don't use x for multiplication. * would work better. :)