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.
Prove is differentiable and find the derivative.
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 .