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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.

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.

To calculate the directional derivative for a specific vector, multiply each partial derivative by the corresponding component of the direction vector and sum them. For $v=[-1,2]$, this means taking -1 times the partial derivative with respect to x, plus 2 times the partial derivative with respect to y.

Conditions: The function $f(x,y)$ is differentiable.; The direction vector is $v=[-1,2]$.; The partial derivatives ∂$f/x$ and ∂$f/y$ exist.

To calculate the directional derivative for a specific vector, multiply each partial derivative by the corresponding component of the direction vector and sum them. For $v=[-1,2]$, this means taking -1 times the partial derivative with respect to x, plus 2 times the partial derivative with respect to y.

Conditions: The function $f(x,y)$ is differentiable.; The direction vector is $v=[-1,2]$.; The partial derivatives ∂$f/x$ and ∂$f/y$ exist.