Derivatives
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[edit] Derivative of a function f at a number a
[edit] Notation
We denote the derivative of a function f at a number a as 
.
[edit] Definition
The derivative of a function f at a number a a is given by the following limit (if it exists):
An analagous equation can be defined by letting x = (a + h). Then h = (x − a), which shows that when x approaches a, h approaches 0:
[edit] Interpretations
[edit] As the slope of a tangent line
Given a function 
, the derivative can be understood as the slope of the tangent line to f(x) at x = a:
[edit] As a rate of change
The derivative of a function f(x) at a number a can be understood as the instantaneous rate of change of f(x) when x = a.
[edit] At a tangent to one point of a curve
[edit] Vocabulary
The point A(a ; f(a)) is the point in contact of the tangent and Cf.
[edit] Definition
If f is differentiable in a, then the curve C admits at a point A which has for coordinates (a ; f(a)), a tangent : it is the straight line passing by A and of direction coefficient f'(a). An equation of that tangent is written: y = f'(a)*(x-a)+f(a)
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