85 - Partial Derivatives of Vector-Valued Functions
When a vector has a multidimensional input and output you can take its partial derivative by simply taking the partial derivative for each of the components.
Vector Valued Functions could represent parametric surfaces. That is, the output is a vector and depending on the parameter it goes along a region of space that is surface.
The partial derivative of a parametric surface vector in a sense is the derivative moving along this surface along that parameter's direction,.
We will see that partial derivatives of vector valued functions give a plane tangent to the surface.