Compute the directional derivatives of each of the following; you may use any of the methods in this section. (a) f(x₁, x₂) = 1 − 2x1 + 3x2 at (2, -1) in the direction (3, 4) (b) q(x, y) = 7+ x² − 2y² at (1, 1) in the direction (1, -1) (c) h(x, y) = (1 + x² + y²)−¹ at (1, 2) in the direction (1,0) (d) f(r, s) = 1 - 3r+rs at (0,6) in the direction (0, 1) (e) k(x, y) = xsin y at (1,7) in the direction (0, 1) (f) y(x₁, x2, x3) = x² + 2x² + 3x3 at (0, 0, -1) in the direction (2,2,1) (g) u(x, y, z) = xyz at (1,0, 3) in the direction (3, 2, -6) (h) p(x, y, z) = xye³+² at (1,3,-3) in the direction (4, -2,4).
Compute the directional derivatives of each of the following; you may use any of the methods in this section. (a) f(x₁, x₂) = 1 − 2x1 + 3x2 at (2, -1) in the direction (3, 4) (b) q(x, y) = 7+ x² − 2y² at (1, 1) in the direction (1, -1) (c) h(x, y) = (1 + x² + y²)−¹ at (1, 2) in the direction (1,0) (d) f(r, s) = 1 - 3r+rs at (0,6) in the direction (0, 1) (e) k(x, y) = xsin y at (1,7) in the direction (0, 1) (f) y(x₁, x2, x3) = x² + 2x² + 3x3 at (0, 0, -1) in the direction (2,2,1) (g) u(x, y, z) = xyz at (1,0, 3) in the direction (3, 2, -6) (h) p(x, y, z) = xye³+² at (1,3,-3) in the direction (4, -2,4).
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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do b) d) f) H)
Transcribed Image Text:Compute the directional derivatives of each of the following; you may use
any of the methods in this section.
(a) f(x₁, x₂) = 1 − 2x1 + 3x2 at (2, -1) in the direction (3, 4)
(b) q(x, y) = 7+ x² − 2y² at (1, 1) in the direction (1, -1)
(c) h(x, y) = (1 + x² + y²)-¹ at (1, 2) in the direction (1,0)
(d) f(r, s) = 1 - 3r+rs at (0,6) in the direction (0, 1)
(e) k(x, y) = xsin y at (1,7) in the direction (0, 1)
(f) y(x₁, x2, x3) = x² + 2x² + 3x3 at (0, 0, -1) in the direction (2,2,1)
(g) u(x, y, z) = xyz at (1,0, 3) in the direction (3, 2, -6)
(h) p(x, y, z) = xye³+² at (1,3,-3) in the direction (4, -2,4).
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