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Derivative Definition
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Main Concept
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Given a function  , its derivative, denoted  or  , is a new function describing the rate of change of  .
The value of the derivative  at any point  is defined by the following limit, if it exists:
Geometrically,  describes the slope of the tangent to the graph of  .
You can find an approximation to the value of the derivative by ignoring the limit:
This expression is the slope of the secant from P =  to a nearby point such as Q =  , and the approximation improves as  becomes smaller.
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Drag the sliders to change the values of x and h. Observe what occurs when h approaches 0.
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