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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.