Findthedirec4onalderiva4veof f x y x ln y 2 y 3

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Unformatted text preview: rem:
 Assume
that
f
is
a
differen4able
func4on
and
 
u=u1i+u2j
is
a
unit
vector.
The
direc4onal
 deriva4ve
of
f
at
a
point
(a,b)
in
the
direc4on
u
is
 given
by

 Du f ( a, b) = f x ( a, b) u1 + f y ( a, b) u2 €€ The
Direc4onal
Deriva4ve
 Example
(revisited):
 #19.
Find
the
direc4onal
deriva4ve
of
 f ( x, y ) = at
the
point
A(‐2,‐2)
in
the
direc4on
of
the
 vector
v=‐i+j.

 € € x 2+ y 2 The
Direc4onal
Deriva4ve
 Example:
 #21.
Find
the
direc4onal
deriva4ve
of
 f ( x, y ) = x ln y + 2 y − 3 






























at
the
point
A(3,5)
in
the
 direc4on
of
the
vector
v=8i+6j.

 2 € € Maximum
and
Minimum
Values
 Defini'on:
 A
func4on
of
two
 variables
has
a
local
 maximum
at
(a,b)
if
 












...
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