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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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) =
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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