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The directional derivative in the direction of a vector w is equal to the dot product of w and the gradient vector ∇f. The gradient vector contains the partial derivatives of the function as its components.

Conditions: The function $f(x,y)$ is differentiable.; The direction vector is $w=[a,b]$.; The gradient ∇f = [∂f/∂x, ∂f/∂y] exists.

The directional derivative in the direction of a vector w is equal to the dot product of w and the gradient vector ∇f. The gradient vector contains the partial derivatives of the function as its components.

Conditions: The function $f(x,y)$ is differentiable.; The direction vector is $w=[a,b]$.; The gradient ∇f = [∂f/∂x, ∂f/∂y] exists.