The directional derivative in the direction of a general vector w=[a,b] is the linear combination of the partial derivatives weighted by the components of w. The formula is a*(∂f/∂x) + b*(∂f/y).
Conditions: The function f(x,y) is differentiable.; The direction vector is w=[a,b].; The partial derivatives ∂f/x and ∂f/y exist.
The directional derivative in the direction of a general vector w=[a,b] is the linear combination of the partial derivatives weighted by the components of w. The formula is a*(∂f/∂x) + b*(∂f/y).
Conditions: The function f(x,y) is differentiable.; The direction vector is w=[a,b].; The partial derivatives ∂f/x and ∂f/y exist.
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.