The directional derivative

Consider a point

in the domain of

. Now suppose you "move through"

in the direction indicated by some unit vector

. As you move through

in the direction of

, what is the rate of change of

? This is the idea behind the directional derivative. No longer are we constrained to move only in the positive

or positive

direction to find the rate of change of

. The derivative of

at the point

in the direction of

is denoted

. In the interactive figure, drag the end of the

vector to change it. Note the axis labels in the bottom-right pane; the horizontal axis indicates distance away from

in the direction of

Developed for use with Thomas' Calculus, published by Pearson.

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