Derivative
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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 |
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Let  and  be a function. Then the derivative of f is a function  defined by:
The derivative is undefined when this limit does not exist, that is, f is not differentiable. |
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Properties
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If 
(or a constant function) and 
are both differentiable on some set D', then so are cf, f + g, − f, and fg. If, in addition, g is nonzero on D', then 
(and also 
) are differentiable on D'. Also, if f is differentiable on 
, then 
is differentiable on D'. In fact:
- c' = 0
(Linearity)
(Linearity)
(Product Rule)
(Quotient Rule)
(Chain Rule)
(See also: Derivative formulas)
Examples:
- 2x differentiated equals 2
- 4x3 differentiated equals 12x2(because 4*3 = 12, and 3-1 = 2)
In graphs, the derivative of a function f at a number a is equal to the slope of the tangent line of the graph of f at the point (a,f(a)).
