# Chain Rule

## Homework Statement

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

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

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diazona
Homework Helper
Use the product rule ;-) (or quotient rule, if you prefer) It generates two terms, but you only found one of them.

Like diazona says, the product rule (combined with your chain rule) shall set you free!

If it was simply

$$f(x)=(3-x^2)^{-2}$$

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).

Thank you very much guys! I see where I went wrong. I appreciate your help, thanks again :)