How do I use the chain and product rules together?

[Griffin-Der]

Ok, I have having a very hard time finding the derivative of this, I have no clue how to do the set up.

x^2(sqrt(9-x^2))

(sorry it's written like that I just have no clue how to type it normally)
So the problem I am having is When do I use the chain rule, and the product rule cohesively, I have the answer to the problem but it does me no good because I cannot solve it.
Thanks in advance.

 

[Griffin-Der]

Any help would be greatly appreciated, I have been pulling my hair out for 2 hours :(

 

[Mark44]

You have a product, so you need to use the product rule first. One of the factors is a composite function, so after you use the product rule, you'll need to use the chain rule.

Don't try to do everything at once.

d/dx[x^2 * (9 - x^2)^(1/2)] = x^2 * d/dx[(9 - x^2)^(1/2)] + 2x * (9 - x^2)^(1/2) = ?

 

[Griffin-Der]

Thank you so much that cleared it right up for me :)