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O Using part (a), compute the directional derivative of f in the following case: 12 3 4 f(x, y, z) = x, x= (e, e, 0), v = i+ Ti+ k 13 13° 13

O Using part (a), compute the directional derivative of f in the following case: 12 3 4 f(x, y, z) = x, x= (e, e, 0), v = i+ Ti+ k 13 13° 13

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 (b)
(a) Assume that f : R3 → R is differentiable. Prove that the directional derivative at x in the direction of a unit vector v is Vƒ(x) · v. (b) Using part (a), compute the directional derivative of f in the following case: 12 V = 13 3 4 f(x, y, z) = xv², = (e, e, 0), i+131+ k 13 %3|
Transcribed Image Text:(a) Assume that f : R3 → R is differentiable. Prove that the directional derivative at x in the direction of a unit vector v is Vƒ(x) · v. (b) Using part (a), compute the directional derivative of f in the following case: 12 V = 13 3 4 f(x, y, z) = xv², = (e, e, 0), i+131+ k 13 %3|
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