 Derivative Definition - Maple Programming Help

Home : Support : Online Help : Math Apps : Calculus : Differential : MathApps/DerivativeDefinition

Derivative Definition

 Main Concept Given a function $f\left(x\right)$, its derivative, denoted $\frac{\mathrm{df}}{\mathrm{dx}}$ or $f'\left(x\right)$, is a new function describing the rate of change of $f\left(x\right)$.   The value of the derivative $\frac{\mathrm{df}}{\mathrm{dx}}$ at any point $x$ is defined by the following limit, if it exists: Geometrically, $\frac{\mathrm{df}}{\mathrm{dx}}$ describes the slope of the tangent to the graph of  $f\left(x\right)$.   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 = $\left(x+h,f\left(x+h\right)\right)$, 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 =







 More MathApps