Suppose that f(x)=x^2 and g(x)=|x|. Then the composites (f ∘g)(x)=|x|^2=x^2 and (g …̧

Suppose that f(x)=x^2 and g(x)=|x|. Then the composites (f ∘g)(x)=|x|^2=x^2 and (g ∘f)(x)=|x^2|=x^2 are both differentiable at x=0 even though g itself is not differentiable at x=0. Does this contradict the Chain Rule? Explain.

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