Using the Chain Rule to Differentiate f(g(x^2))

[jesuslovesu]

I'm a little confused as to when to stop taking the derivative of the inside function when using the chain rule...

Lets say I have f( g(x^2) )

Would this be correct?
f`( g(x^2) ) * g`(x^2) * 2x ?

Or do I keep on going until the x is completely gone from the equation?

 

[DaMastaofFisix]

nope, you're done. The idea here is that you only differentiate the functions given. You can't assume that there are still more. All this is is a double composite. It could have been written as F(g(h(x)), which is the same as before except with replcing th x^2 with h(x). Just do the setup and don't second guess yourself.