(a) Sketch the dependency diagram for w = f(x, y, z) = 3.xyz – y²z, with x = 2t + s, y = -t – s, z = ť² + s². Then find the partial derivatives of w with respect to each of the variables x, y, s and t.

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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2. (a) Sketch the dependency diagram for w =
f(x, y, z) = 3xyz – y²z, with x = 2t + s,
y = -t – s, z = t² + s². Then find the partial derivatives of w with respect to
each of the variables x, y, s and t.
g(u, v) where u = xy and v = x/y. Sketch the dependency diagram and
dw
(b) Let w =
then express and u in terms of x, y, gu and g,.
ду
Transcribed Image Text:2. (a) Sketch the dependency diagram for w = f(x, y, z) = 3xyz – y²z, with x = 2t + s, y = -t – s, z = t² + s². Then find the partial derivatives of w with respect to each of the variables x, y, s and t. g(u, v) where u = xy and v = x/y. Sketch the dependency diagram and dw (b) Let w = then express and u in terms of x, y, gu and g,. ду
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