Multivalued Function Gradient
Multivariable Functions’ derivatives change according to which way you move. However, the gradient of a multivariable function is basically the direction/vector in which the gradient is maximal. It is basically calculated as such:
$$ \triangledown f(x,y) = \langle \frac{\partial f}{\partial x}(x,y), \frac{\partial f}{\partial y}(x,y) \rangle $$