Finding the Derivative of x(3-x^2)^-2

[Oscar Wilde]

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

 

[diazona]

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

 

[phyzmatix]

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).

 

[Oscar Wilde]

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