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:
limh→0 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:
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.
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