A vector function is any function whose output is a vector. Parametric equations are often represented as vector functions in the following manner. This example has a single input () and produces three simultaneous outputs all which are functions of in themselves. The sum of the three components produces the radius vector. Another example would be a vector function with coordinates as inputs, in the form This equation represents a two-dimensional vector field. The derivative of a vector function is equal to The integral of a vector function is equal to