$f_n(x) = \dfrac{nx^2 + 1}{2n + x}$, assume $f_n$ converges to $f$ and $f'_n$ converges to $g$ pointwisely. Then $f' = g$ on a compact subset of reals

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$f_n(x) = \dfrac{nx^2 + 1}{2n + x}$, assume $f_n$ converges to $f$ and $f'_n$ converges to $g$ pointwisely. Then $f' = g$ on a compact subset of reals

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