# Question about the meaning of derivative .

1. Jan 26, 2013

### thewoodpecker

Hello

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.

Last edited by a moderator: Jan 26, 2013
2. Jan 26, 2013

### rollingstein

3. Jan 27, 2013

### thewoodpecker

Please if someone see something wrong in my statement, correct it.

4. Jan 28, 2013

### Staff: Mentor

What does "distance as one point" mean? Distance is a measure of how far one point is from another point.

5. Jan 28, 2013