Derivative Definition - Maple Programming Help

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Derivative Definition

Main Concept

Given a function fx, its derivative, denoted dfdx or f'x, is a new function describing the rate of change of fx.

 

The value of the derivative dfdx at any point x is defined by the following limit, if it exists:

limh0 fx+h fxh

Geometrically, dfdx describes the slope of the tangent to the graph of  fx.

 

You can find an approximation to the value of the derivative by ignoring the limit:

 

fx+h fxh

 

This expression is the slope of the secant from P = x,fx to a nearby point such as Q = x+h,fx+h, and the approximation improves as h becomes smaller.

 

Drag the sliders to change the values of x and h. Observe what occurs when h approaches 0.

 

 

 

 

 

 

h =

x =

slope =

 

 

 

 

 

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