Thread: check d differentiability

will d following function be differentiable at x = 0 ???
1. cos(|x|)+|x|
2. sin(|x|)-|x|

Hi

First one:

If approaches zero from the right, we have:



Now we approach from the left. Note that , is an even function.



So the function is not differentiable at .

The second one you basically do the same thing.

and

.

So the second one is differentiable.