Definition:Derivative/Vector-Valued Function

On an Open Set
Let $\mathbf r: t \mapsto \mathbf r \left({t}\right)$ be a vector-valued function defined for all $t$ on some real interval $\mathbb I$.

The derivative of $\mathbf r$ with respect to $t$ is defined as the limit:

for all $t$ for which the limit exists. .

Also see

 * Definition:Jacobian Matrix
 * Differentiation of Vector-Valued Function Componentwise