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
.