Define $f:\mathbb{R}\to \mathbb{R}$ by $$f(x)=\{\begin{array}{ll}(1-\cos x)\sin \left(\frac{1}{x}\right),& x\ne 0\\ 0,& x=0\end{array}$$ Then,$$ (a) $f$ is discontinuous. $$ (b) $f$ is continuous but not differentiable. $$ $$ $$ (c) $f$ is differentiable and its derivative is discontinuous. $$ $$ $$$$$$ $$ (d) $f$ is differentiable and its derivative is continuous.