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I know that the definition of a derivative at given point is the limit of the difference quotient as Δx goes to zero.

I just want to be sure, that I have understood it right. So i have this question.

Is the derivative at a given point is the ratio of change of dependent variable and change of independent variable over a so small distance (infinitely small) that we can assume this ratio(slope) does not change in that distance, and we can look at this distance as one point.

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# Question about the meaning of derivative .

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