The function f(x)=(x−1)|x−1|+sin⁡(|x|) is

Functions in |x| is not differentiable at x=0 but x x is differentiable ∀x Function (x−1)|x−1| is differentiable at all points.  So, function f(x)=|x−1|(x−1)+sin⁡|x| is not differentiable at x=0 only.