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**For tiny h, f(x+h) = f(x) + hf'(x) ??**

Hi all

I've been reading about proof of the chain rule and something is making me not sleep at night..

How is that possible that: "for tiny h, f(x+h) = f(x) + hf'(x)" ?

Even if 'h' is ultra-small, then "f(x+h)" will always differ from "f(x) + hf'(x)"... I know - the smaller the 'h', the smaller the difference but the difference will always exist for 'h' not equal to zero... So how can we plug this: "f(x) + hf'(x)" instead of "f(x+h)"..

Can someone explain this to me?