Is there any function in this way? $f$ is a function which is continous on $\Bbb R$, and $f^2$ is differentiable at $x=0$. Suppose $f(0)=1$. Must $f$ be differentiable at $0$? 
I may feel it is not necessarily for $f$ to be differentiable at $x=0$ though $f^2$ is. But I cannot find a counterexample to disprove this. Anyone has an example? 

Hint:
$$\frac{f(x)-1}{x}=\frac{f(x)^2-1}{x}\frac{1}{f(x)+1}\xrightarrow [x\to 0]{}...?$$
