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Chain Rule

  • #1

Homework Statement



I am supposed to find the derivative of: x(3-x^2)^-2

Homework Equations



The chain rule

The Attempt at a Solution



Well I feel that I am good at using the chain rule but something tells me I can't use it here, because when I do, I only get about half of the answer.

But anyway, I multiplied x by -2 , which I multiplied by the group (3-x^2)^-3. Then I multiplied that term by the derivative of the first group, (3-x^2), and got: 4x^2 * (3-x^-2)^-3

however, the right answer is listed as: 4x^2 *(3-x^2)^-3 + (3-x^2)^-2

for some reason I don't think the chain rule applies to this problem? or perhaps I am doing it wrong... I would appreciate any help or explanation
 

Answers and Replies

  • #2
diazona
Homework Helper
2,175
6
Use the product rule ;-) (or quotient rule, if you prefer) It generates two terms, but you only found one of them.
 
  • #3
299
0
Like diazona says, the product rule (combined with your chain rule) shall set you free! :smile:

If it was simply

[tex]f(x)=(3-x^2)^{-2}[/tex]

then the chain rule would have sufficed.

However, you have two terms involving x that are multiplied with each other so you also need to incorporate the product rule (or quotient rule for this particular case, but I'd personally prefer the product rule).
 
  • #4
Thank you very much guys! I see where I went wrong. I appreciate your help, thanks again :)
 

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