Directional Derivatives and the Gradient
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This Demonstration visually explains the theorem stating that the directional derivative of the function
at the point
,
) in the direction of the unit vector
is equal to the dot product
of the gradient of
with
. If we denote the partial derivatives of
at this point by
and
and the components of the unit vector
by
and
, we can state the theorem as follows:
Contributed by: Bruce Torrence (March 2011)
Open content licensed under CC BY-NC-SA
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