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Real Analysis : Differentiability

Prove that if f and g are differentiable functions on an interval A and satisfy f'(x)=g'(x) for all x belong to A, then f(x)=g(x)+k for some constant k belong to R.

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We know if a function h(x) is differentiable on an interval A and h'(x)=0, then h(x) is a ...

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Differentiability is investigated