Let z(x, y) = x³y where x = t³ & y = tº. dz dx dy by first finding & and using the chain rule. dt dt dt Calculate dx dt dy dt Now use the chain rule to calculate the following: dz d.t Question Help: Video =
Let z(x, y) = x³y where x = t³ & y = tº. dz dx dy by first finding & and using the chain rule. dt dt dt Calculate dx dt dy dt Now use the chain rule to calculate the following: dz d.t Question Help: Video =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![### Chain Rule (One Independent Variable)
Consider the function \( z(x, y) = x^5 y \) where \( x = t^8 \) and \( y = t^6 \).
**Objective**: Calculate \(\frac{dz}{dt}\) by first finding \(\frac{dx}{dt}\) and \(\frac{dy}{dt}\) and then using the chain rule.
#### Steps
1. Differentiate \( x = t^8 \) with respect to \( t \):
\[
\frac{dx}{dt} =
\]
2. Differentiate \( y = t^6 \) with respect to \( t \):
\[
\frac{dy}{dt} =
\]
3. Now use the chain rule to calculate:
\[
\frac{dz}{dt} =
\]
**Need Help?** Watch the instructional video for guidance.
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Transcribed Image Text:### Chain Rule (One Independent Variable)
Consider the function \( z(x, y) = x^5 y \) where \( x = t^8 \) and \( y = t^6 \).
**Objective**: Calculate \(\frac{dz}{dt}\) by first finding \(\frac{dx}{dt}\) and \(\frac{dy}{dt}\) and then using the chain rule.
#### Steps
1. Differentiate \( x = t^8 \) with respect to \( t \):
\[
\frac{dx}{dt} =
\]
2. Differentiate \( y = t^6 \) with respect to \( t \):
\[
\frac{dy}{dt} =
\]
3. Now use the chain rule to calculate:
\[
\frac{dz}{dt} =
\]
**Need Help?** Watch the instructional video for guidance.
[Submit Question Button]
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