Topics: Vector-Valued Function - Calculus


Let be a vector-valued function.

The derivative of is defined by:

…for any values of for which the limit exists. When the limit as exists, we say that is differentiable at .

We can also derivate operated vector-valued functions.


If we develop the limit given in this definition, we’ll find that, if , then:

Graphical Representation

Graphically, the derivative of a vector-valued function is the tangent vector to the function’s curve at .