Let and be differentiable functions for all
Now if , can I conclude that because is differentiable,
thus is differenitable.
And further that if is differentiable then:
and thus is twice differentiable?
If not, then how about if is bijective and thus has an inverse , and the inverse is differentiable.
Then:
And now is a combination of 2 differentiable functions, thus
then is twice differentiable?
This is not homework, I am just thinking.