This is a homework problem on the Algebra of Derivatives section in my text. I'm not sure if I'm handling the

part correctly. Any suggestions (or if it's right, let me know) would help ease my mind greatly.

__Problem__ is differentiable.

Prove

is differentiable and find the derivative.

__Proof__
We know that

is differentiable over the real numbers, and clearly, if

is a real number, then

is a real number, so

is differentiable. Let

. Then

is differentiable, and by the Algebra of Derivatives,

must be differentiable.

It follows from the product rule that

.