Which of the following functions is differentiable at $x=0$?
Step-by-Step Solution
Key Concept: Check LHD$=$RHD at $x=0$ for each. $\tan|x|,\sin|x|,\cos|x|$ are all even functions. The expression inside $|\cdot|$, differentiated at $0$: LHD$=-$RHD for odd part. $f(x)=|\sin|x|-\tan|x||$: both $\sin|x|$ and $\tan|x|$ have same sign near 0, difference $\approx-x^3/6$. $|{-x^3/6}|$ is differentiable at 0.
$|\sin|x|-\tan|x||$ is differentiable at $x=0$.
Correct Answer: 2