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Let w(x, y, z) = x² + y² + z² where x = Calculate dx dt dy dt dz dt = dw dt || by first finding sin(- 6t), y Now use the chain rule to calculate the following: dw dt = cos (9t), z = e dx dy dz & and using the chain rule. dt dt dt "

Let w(x, y, z) = x² + y² + z² where x = Calculate dx dt dy dt dz dt = dw dt || by first finding sin(- 6t), y Now use the chain rule to calculate the following: dw dt = cos (9t), z = e dx dy dz & and using the chain rule. dt dt dt "

Advanced Engineering Mathematics
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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Let w(x, y, z) = x² + y² + z² where x 2 Calculate by first finding dw dt dx dt dy dt || || dx dy dt' dt || = : sin( – 6t), y = cos(9t), z = e dz dt and using the chain rule. dz dt Now use the chain rule to calculate the following: dw dt
Transcribed Image Text:Let w(x, y, z) = x² + y² + z² where x 2 Calculate by first finding dw dt dx dt dy dt || || dx dy dt' dt || = : sin( – 6t), y = cos(9t), z = e dz dt and using the chain rule. dz dt Now use the chain rule to calculate the following: dw dt
Expert Solution
Step 1

Using the chain rule, it can be written that: ddxf(g(x))=f'(g(x))×g'(x).

It is known that: 

ddxsinkx=kcoskxddxcoskx=-ksinkxddxekx=kekx

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