Derivative

The instantaneous rate of change of a function
f (x) at a particular point
x_{0}, denoted
f'(x_{0}) or
(x_{0}). The formal definition is the following limit:
f'(x_{0}) = 

Derivative Function

A function f'(x) taking on the value of the derivative of f (x) at each number x.
Difference Quotient

For a function
f, and any two points
x_{0} and
x in its domain, the quotient:
Differentiable

A function f is differentiable at a point (x_{0}) if it has a welldefined derivative
at that point. It is simply differentiable if it is differentiable at every point in its
domain.
Secant Line

A line through two distinct points on the graph of a function.
Tangent Line

A line through a point (x, f (x)) on a graph that has slope equal to the derivative of the
function f at x. A limit of secant lines to the graph of a function as two contact
points approach one another.