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Gradient
See also Laplacian Operator
En vektor der peger i $x$-$y$-planet, til den stejlsete side
$$\nabla f(x_0,y_0)=\v{f_x'(x_0,y_0)}{f_y'(x_0,y_0)}$$
To get the rate of change ($h$) in a specific direction in a point, you can project the gradient onto the unit vector in the direction ($\hat{\vec v}$).
$$h = \hat{\vec v} \bullet \nabla f(x_{0}, y_{0})$$
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