The gradient of a function (denoted $ \nabla f(x_1, x_2, \cdots , x_n) $) is the multivariate equivalent to the first derivative of a single variable function. The gradient is a vector where each entry is a partial differentiation of the original function. For a function $ f(x_1, x_2, \cdots , x_n) $, the gradient is defined as:
$ (\frac{\partial f}{x_1}, \frac{\partial f}{x_2}, \cdots, \frac{\partial f}{x_n}) $
