The directional derivative of
in the direction of
,
a unit vector:
In
,
for
and
,
a unit vector:
The gradient vector
or
The del operator
Dot product representation of the directional derivative
Find the directional derivative of at the point in the direction .
Find the directional derivative of the function at the point in the direction .
Characteristics of the gradient vector
points in the direction of maximum change of
The maximum rate of change of at is
Tangent plane and normal line to a level surface at the point
Tangent plane:
Normal line:
Find equations of (a) the tangent plane and (b) the normal line
to the surface
at the point
.