What would you like to understand?

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.