How do I find the solution to this derivative problem?

  • Thread starter Cuisine123
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  • #1
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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.
 

Answers and Replies

  • #2
537
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Have you learned the chain rule yet?

My hint is: what is the derivative of
[tex]\frac{1}{[g(x)]^2}?[/tex]
 
  • #3
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Have you learned the chain rule yet?

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

Is it -2g(x)^-3 x g(x)?
 
  • #4
Hint #2:
Chain rule: f(g(x)) = f'(g(x))g'(x)

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

Soooo....
 
  • #5
537
3
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. :)
 

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