In this case we have

(*)

Now and are compositions of functions so do need the Chain Rule (see “Chain Rule by Rule”: http://irishjip.wordpress.com/2010/10/26/the-chain-rule/)

“differentiate the outside function with respect to the inside, and then multiply by the derivative of the inside”

.

Similarly,

.

Going back to (*):

as you said.

Regards,

J.P.