I understand derivatives and I am not trying to be like a stickler or anything, but before manipulating the equation to arrive at a form where we can find a real answer for a derivative, we are left with [f(x+h)-f(x)]/h (where h is delta x I guess as most people write it). Before evaluating it further, if we are taking the limit as h goes to zero....then wouldn't the equation, which once manipulated gives us a reasonable answer, be equal to (0-0)/0 for all derivatives? Why is it that we are allowed to ignore this form and use the manipulated form?(adsbygoogle = window.adsbygoogle || []).push({});

I hope my question was clear, thanks in advance.

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# Can it be argued that derivatives should be undefined?

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