Gradient

The gradient of $f$ is the vector of partial derivatives as $$\nabla f(\mathbf{x}) = \begin{bmatrix}\frac{\partial f}{\partial x_1}(\mathbf{x})\\ \vdots \\\frac{\partial f}{\partial x_d} (\mathbf{x})\end{bmatrix}$$

Also see: Hessian matrix

References:

1. https://www.chrismusco.com/amlds2023/notes/lecture06.html