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

Let $f(x)=x|x|, g(x)=\sin x$ and $h(x)=$ $(g o f)(x)$. Then

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

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

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

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


Correct Option: 2,

Solution:

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