Let u(æ, y, z) = Vr +y + z? where æ = 8re', y = 2te & z = et, du ду dw E Ər ot Әх ду дz Әх or ' or ' Or ' ot . > ot Calculate dw dw Ət by first finding 64re + +tert √64r²e²t+41²e²r + 2rt V 41²2r -8ret (−8re) + (2ter) + (et)2 (−8e') + & dz t and using the chain rule. 2te ਵਿਅੰਗ ( # (2te) + 8re) + (2ter)? + (et)2 ert 8ret) + (2ter) + (et)? ਹੈ (tert) E
Let u(æ, y, z) = Vr +y + z? where æ = 8re', y = 2te & z = et, du ду dw E Ər ot Әх ду дz Әх or ' or ' Or ' ot . > ot Calculate dw dw Ət by first finding 64re + +tert √64r²e²t+41²e²r + 2rt V 41²2r -8ret (−8re) + (2ter) + (et)2 (−8e') + & dz t and using the chain rule. 2te ਵਿਅੰਗ ( # (2te) + 8re) + (2ter)? + (et)2 ert 8ret) + (2ter) + (et)? ਹੈ (tert) E
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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Question
Transcribed Image Text:Let w(x, y, z) = √x² + y² + z² where x= -8ret, y = 2te' & z = ert.
дw
дw
& by first finding
St
Әх ду дz Әх ду
ar'ar'ar' at
"
Or
Ət
Calculate
dw
ar
dw
at
64re2t + 4²e2r + te2rt
+
√64r2e2t + 4+²e2r 2rt
+
-8ret
-8ret)2 + (2ter)2 + (ert) 2 )
Submit Question
(-8e') +
дz
Hint: Recall the chain rule: For z(x(s, t),y(s, t)), we have
2t
Q Search
&
дz
St
and using the chain rule.
2ter
(-8ret)2 + (2ter)2 + (ert) 2
дz Əх
3x Ht
+
дz
ду
EA
(2ter) +
Oy
Ot
(ww.rus
ert
-8ret)2 + (2ter)2 + (ert) 2,
В
H
(tert)
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