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Show that the function $g(x) = x^2 \sin\left(\frac{1}{x}\right) ,(g(0) = 0)$ is everywhere differentiable and that $g′(0) = 0$.

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    possible duplicate of [Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$](http://math.stackexchange.com/questions/393602/differentiability-of-fx-x2-sin-frac1x-and-f)2014-03-01
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    @TuckerRapu: The dependency is the other way around; this question is older than the one you've linked.2014-04-09

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