1 Find af /dx, Əf / dy if ар лах а fax,y) - ху bfcxy)= exy cЈ fexiys - x cosx cosy d.j fexiyo= (хвучу вод (x2+y?). tỷ
1 Find af /dx, Əf / dy if ар лах а fax,y) - ху bfcxy)= exy cЈ fexiys - x cosx cosy d.j fexiyo= (хвучу вод (x2+y?). tỷ
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
A,b,c
![Etol villa
20
morenability for Functions of Two Variables
Using the linear approximation, we are ready to define the notion of differentiability.
Definition Differentiable: Two Variables Let f: R² → R. We say f is
differentiable at (xo, yo), if af/ax and af/ay exist at (xo, yo) and if
f(x, y)-f(xo, yo) -
[af
əx
f(xo, yo) +
-(xo, yo) (x-xo) -
||(x, y) - (xo, yo) ||
[af (x -
-(xo, yo)
əx
- x0) +
af
as (x,y) → (xo, yo). This equation expresses what we mean by saying that
[af
Jo) ] (Y - YO)
yo)
ду
is a good approximation to the function f.
-(xo, yo) (y-yo)
Əy
-0
-(xo, yo)
(2)
polecon
bour ow isdi tuo a
It is not always easy to use this definition to see whether f is differentiable, but it
will be easy to use another criterion, given shortly in Theorem 9.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa03415f8-38f2-4478-b688-afaca619ca5c%2F38386b07-d931-46c4-a684-88692ecd987c%2Fhi42htb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Etol villa
20
morenability for Functions of Two Variables
Using the linear approximation, we are ready to define the notion of differentiability.
Definition Differentiable: Two Variables Let f: R² → R. We say f is
differentiable at (xo, yo), if af/ax and af/ay exist at (xo, yo) and if
f(x, y)-f(xo, yo) -
[af
əx
f(xo, yo) +
-(xo, yo) (x-xo) -
||(x, y) - (xo, yo) ||
[af (x -
-(xo, yo)
əx
- x0) +
af
as (x,y) → (xo, yo). This equation expresses what we mean by saying that
[af
Jo) ] (Y - YO)
yo)
ду
is a good approximation to the function f.
-(xo, yo) (y-yo)
Əy
-0
-(xo, yo)
(2)
polecon
bour ow isdi tuo a
It is not always easy to use this definition to see whether f is differentiable, but it
will be easy to use another criterion, given shortly in Theorem 9.
Transcribed Image Text:a
1) Find af lax, Əf/ dy if
• f(x,y) = xy
bfexiy), exy
cЈfexrys - xcosx cозу
d.j fexiyo= (x'учу вод (x'tу ?).
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