Find ôw/as and aw/at using the appropriate Chain Rule. Function Values w = y3 – 6x?y x = e, y = et s = -4, t = 8 aw as aw at Evaluate each partial derivative at the given values of s and t. aw as at ||
Find ôw/as and aw/at using the appropriate Chain Rule. Function Values w = y3 – 6x?y x = e, y = et s = -4, t = 8 aw as aw at Evaluate each partial derivative at the given values of s and t. aw as at ||
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
![**Find \(\partial w/\partial s\) and \(\partial w/\partial t\) using the appropriate Chain Rule.**
**Function**
\[ w = y^3 - 6x^2y \]
\[ x = e^s, \quad y = e^t \]
**Values**
\[ s = -4, \quad t = 8 \]
**Partial Derivatives**
\[
\frac{\partial w}{\partial s} =
\]
\[
\frac{\partial w}{\partial t} =
\]
---
**Evaluate each partial derivative at the given values of \(s\) and \(t\).**
\[
\frac{\partial w}{\partial s} \bigg|_{s=-4, t=8} =
\]
\[
\frac{\partial w}{\partial t} \bigg|_{s=-4, t=8} =
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F124169c6-8d32-433b-ba67-139925e22b98%2F8129ad4a-b41b-4ba5-a81f-5c25f2322391%2Fa6w0ulx_processed.png&w=3840&q=75)
Transcribed Image Text:**Find \(\partial w/\partial s\) and \(\partial w/\partial t\) using the appropriate Chain Rule.**
**Function**
\[ w = y^3 - 6x^2y \]
\[ x = e^s, \quad y = e^t \]
**Values**
\[ s = -4, \quad t = 8 \]
**Partial Derivatives**
\[
\frac{\partial w}{\partial s} =
\]
\[
\frac{\partial w}{\partial t} =
\]
---
**Evaluate each partial derivative at the given values of \(s\) and \(t\).**
\[
\frac{\partial w}{\partial s} \bigg|_{s=-4, t=8} =
\]
\[
\frac{\partial w}{\partial t} \bigg|_{s=-4, t=8} =
\]
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