Derivative/Definition
Revision as of 11:45, 7 September 2006 by JBL (talk | contribs) (Derivative/Mathematical definition moved to Derivative/Formal definition)
The derivative of a function is defined as the instantaneous rate of change of the function at a certain point. For a line, this is just the slope. For more complex curves, we can find the rate of change between two points on the curve easily since we can draw a line through them.
In the image above, the rate of change between the two points is the slope of the line that goes through them: .
We can move the second point closer to the first one to find a more accurate value of the derivative. Thus, taking the limit as goes to 0 will give us the derivative of the function at
:
![$f'(x) = \lim_{h\to 0}\frac{f(x+h)-f(x)}h.$](http://latex.artofproblemsolving.com/8/6/b/86bd376049080d6bd506d0e5955b97b874cfc33f.png)