calculus - Functions not differentiable but continuous

So I have another question about functions:

Question: If neither $f$ nor $g$ is differentiable at $a$, but both are continuous at $a$, then $f+g$ is not differentiable at $a$.

I know that we could have a function $f(a)=|a|$ and $g(a)=|a|$, where $a=0$, so this means $f$ and $g$ are both continuous but not differentiable at $a=0$.

But how do I show that $f+g$ is not differentiable now?
How would I go about this?