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(d) Let f(x, y) = 2x² + xy-y². Prove that the directional derivative of f(x, y) at point x = (3,-2) in the direction v=i- j is 2.

(d) Let f(x, y) = 2x² + xy-y². Prove that the directional derivative of f(x, y) at point x = (3,-2) in the direction v=i- j is 2.

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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please do d

(b) Let r = xi + yj + zk, and let r= ||r. If f is a differentiable function of one variable, show that ▼(f(r)r) = rf'(r) +3f(r) (c) If and are smooth scalar fields, show that ▼x (6V) = Vox V (d) Let f(x, y) = 2x² + xy-y². Prove that the directional derivative of f(x, y) at point x = (3,-2) in the direction v = i- j is ¾.
Transcribed Image Text:(b) Let r = xi + yj + zk, and let r= ||r. If f is a differentiable function of one variable, show that ▼(f(r)r) = rf'(r) +3f(r) (c) If and are smooth scalar fields, show that ▼x (6V) = Vox V (d) Let f(x, y) = 2x² + xy-y². Prove that the directional derivative of f(x, y) at point x = (3,-2) in the direction v = i- j is ¾.
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