Partial Derivatives and Gradients

What are gradients?

A multivariate function in mathematics is a function that takes more than one input variable and produces one or more output variables. For example, the volume of a cylinder $f(x, y) = \pi x^2y$ is a multivariate function because it takes two inputs: the radius $x$ and the height $y$ of the cylinder.

For multivariate functions $f(x) = f(x_1, x_2, ..., x_m)$where the input $x \in \R^m$ ...