Let f(x)=x|x|, g(x)=sin x and h(x)

$h^{\prime}(x)$ is differentiable at $x=0$

$h^{\prime}(x)$ is continuous at $x=0$ but is not differentiable at $x=0$

$\mathrm{h}(\mathrm{x})$ is differentiable at $\mathrm{x}=0$ but $\mathrm{h}^{\prime}(\mathrm{x})$ is not continuous at $\mathrm{x}=0$

$\mathrm{h}(\mathrm{x})$ is not differentiable at $\mathrm{x}=0$