Translations:The directional derivative/5/en

The directional derivative is a generalization of a partial derivative (Robinson and Clark, 2005a). The partial derivatives give the rate of change of the traveltime in the directions of the axes. The directional derivative gives the rate of change in any specified direction. The traveltime $t\left(x,y\right)$ depends on both coordinate axes x, y. We might hold y constant and consider the curve that gives the variation of t with x alone. The slope $\partial {\rm {/}}\partial x$ of this curve is called the partial derivative of t with respect to x. We define the partial derivative $\partial t/\partial y$ similarly.