f′(1)=h→0limhf(1+h)−f(1) ⇒f′(1)=h→0limh(1+h−1)sin(1+h−11)−0=h→0limhhsin(h1)⇒f′(1)=h→0limsin(h1) ∴f is not differentiable at x=1. Similarly, f′(0)=h→0limhf(h)−f(0) ⇒f′(0)=h→0limh(h−1)sin(h−11)−sin(1) ⇒f is also not differentiable at x=0.