2. (a) Prove that the function f(x, y) = xy is differentiable everywhere in its do- %3D x² + y? main. (b) Identify the unit vector u pointing in the direction of maximum increase of the function f(x, y) = e" + y at the point (1, 1).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question2
xy
2. (a) Prove that the function f(x,y)
is differentiable everywhere in its do-
x2 + y²
main.
(b) Identify the unit vector ū pointing in the direction of maximum increase of the
function f(x, y) = e" + y at the point (1, 1).
Transcribed Image Text:xy 2. (a) Prove that the function f(x,y) is differentiable everywhere in its do- x2 + y² main. (b) Identify the unit vector ū pointing in the direction of maximum increase of the function f(x, y) = e" + y at the point (1, 1).
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