Derivative
From Mathematics
The derivative is a concept from calculus that is based on the idea that the graphs of functions look more and more like straight lines as you zoom in.
The process of finding a derivative is called differentiation.
| Definition |
|---|
Let  and  be a function. Then the derivative of  is a function  defined by:
The derivative is undefined when this limit does not exist, that is, |
[edit] Properties
If 
(or a constant function) and 
are both differentiable on some set 
, then so are 
, 
, 
, and 
. If, in addition, 
is nonzero on , then 
(and also 
) are differentiable on . Also, if is differentiable on 
, then 
is differentiable on . In fact:
(Linearity)
(Linearity)
(Product Rule)
(Quotient Rule)
(Chain Rule)
(See also: Derivative formulas)
Examples:
-
differentiated equals 
-
differentiated equals 
(because 4*3 = 12, and 3-1 = 2)
In graphs, the derivative of a function at a number 
is equal to the slope of the tangent line of the graph of at the point 
.
