Definition:Derivative/Vector-Valued Function

Definition
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

 * Differentiation of Vector-Valued Function Componentwise