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The Derivative

Terms

Introduction and Summary

Geometric Definition of Derivative

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 well-defined 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.

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