Compute the gradients of the following functions. (a) f(x, y, z) = 4x exp(-x² - y2 - z²) (Note that exp(u) = e4.) Vf(x, y, z) = (b) f(x, y, z) = 5xyz x² + y² + z² Vf(x, y, z) = (c) f(x, y, z) = 5z²e* cos(y) Vf(x, y, z) =
Compute the gradients of the following functions. (a) f(x, y, z) = 4x exp(-x² - y2 - z²) (Note that exp(u) = e4.) Vf(x, y, z) = (b) f(x, y, z) = 5xyz x² + y² + z² Vf(x, y, z) = (c) f(x, y, z) = 5z²e* cos(y) Vf(x, y, z) =
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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![Compute the gradients of the following functions.
(a) f(x, y, z) = 4x exp(-x² - y² – z²) (Note that exp(u) = e“.)
Vf(x, y, z)
(b) f(x, y, z)
=
=
5xyz
x² + y² + z²
Vf(x, y, z) =
(c) f(x, y, z) = 5z²ex cos(y)
Vf(x, y, z) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f1c68a1-c113-41cc-b0cf-42f2666e5687%2F2dbbc619-1ba2-4d5c-979f-daa61a17c628%2F9zr675d_processed.png&w=3840&q=75)
Transcribed Image Text:Compute the gradients of the following functions.
(a) f(x, y, z) = 4x exp(-x² - y² – z²) (Note that exp(u) = e“.)
Vf(x, y, z)
(b) f(x, y, z)
=
=
5xyz
x² + y² + z²
Vf(x, y, z) =
(c) f(x, y, z) = 5z²ex cos(y)
Vf(x, y, z) =
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