Category:Definitions/Derivatives

This category contains definitions related to Derivatives.
Related results can be found in Category:Derivatives.

Let $I \subset \R$ be an open interval.

Let $f: I \to \R$ be a real function.

Let $f$ be differentiable on the interval $I$.

Then the derivative of $f$ is the real function $f': I \to \R$ whose value at each point $x \in I$ is the derivative $\map {f'} x$:

$\ds \forall x \in I: \map {f'} x := \lim_{h \mathop \to 0} \frac {\map f {x + h} - \map f x} h$