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Question about the meaning of derivative . 
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#1
Jan2613, 11:08 AM

P: 3

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. 


#2
Jan2613, 02:01 PM

PF Gold
P: 330

Sounds good to me broadly.



#3
Jan2713, 10:06 AM

P: 3

Hi, thanks for the reply.
Please if someone see something wrong in my statement, correct it. 


#4
Jan2813, 08:58 AM

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P: 21,258

Question about the meaning of derivative .



#5
Jan2813, 01:19 PM

P: 3

Hi, thanks for the reply.
Would it be correct if i say the two points are infinitely close to each other so we can view at these two points as one point? The distance between them is infinitely small. Thanks for help. 


#6
Jan2813, 02:10 PM

P: 784

The way you should look at it is that you are considering the limit as the difference between two points gets infinitely close to zero but does not become zero. 


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