Question : Test the differentiability of the function $$\cos |x-5|+\sin |x-3|+|x+10|^3-(|x|+4)$$ at the points $5, 3, -10, 0$.
Solution : Now $\cos |x|$ is differentiable everywhere. So is $\sin |x|$ as well as $|x|^3$. Therefore the only issue is the function $|x|$ at $x=0$. Therefor the function is differentiable at all the other points except $x=0$.
Is this correct?