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bj f(x,y)= еху cЈ fexiy>= x cosx cобу p² d.j fexiys= (x'y 2) log (x'ty ?).

bj f(x,y)= еху cЈ fexiy>= x cosx cобу p² d.j fexiys= (x'y 2) log (x'ty ?).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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B,c,d
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: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.
Find af lax, af/ dy if a a) f(x,y) = xy bi f(x,y)= exy c. f(xiy) = x COSX cosy p= lag d.) f(x,y)= (x²+ y²) log (x²+y²).
Transcribed Image Text:Find af lax, af/ dy if a a) f(x,y) = xy bi f(x,y)= exy c. f(xiy) = x COSX cosy p= lag d.) f(x,y)= (x²+ y²) log (x²+y²).
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