The
directional
derivative of a function f at the point
a, b, c
in the
direction
u =
u1, u2, u3
is given by the
inner product of ∇f and
u at the point
a, b, c
. That is, for a vector
u of unit length and a
scalar function f,
Duf![]() ![]() |
= | ∇f![]() ![]() |
|
= | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
To compute the directional derivative of f (x, y, z) = xyz in the direction
CTRL + Evaluate, Evaluate, Evaluate Numerically
∇xyz⋅cos
sin
, sin
sin
, cos
![]()
=yz, xz, xy
⋅
cos
sin
, sin
sin
, cos
![]()
=yz
sin
π +
xz
sin
π + xy cos
π
= .31599yz + .13089xz + .93969xy