Gradient Vector

The gradient vector of a bivariate function is the rate of change of that function, in any direction.

Definition §

$\text{grad }f=\nabla f=(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y})$ Just like the derivate of a 1D (univariate) function requires an x value to return the derivate at that point, a gradient vector requires the coordinate x-y

#tosee why does the gradient vector need to be dotproducted with another vector? why not just sub in the x-y?