дz дz Use the chain rule to find and дл дt' z = x² + xy + y², x = 10s + 6t, y = 3s + 6t First the pieces: дz ºlä ãla əla Әx дх Əs ду дл дz = Əs = And putting it all together: = = дz = дt where ºlò ãlə ələ дz dt ду dt || || ||
дz дz Use the chain rule to find and дл дt' z = x² + xy + y², x = 10s + 6t, y = 3s + 6t First the pieces: дz ºlä ãla əla Әx дх Əs ду дл дz = Əs = And putting it all together: = = дz = дt where ºlò ãlə ələ дz dt ду dt || || ||
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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![Use the chain rule to find \(\frac{\partial z}{\partial s}\) and \(\frac{\partial z}{\partial t}\), where
\[ z = x^2 + xy + y^2, \quad x = 10s + 6t, \quad y = 3s + 6t \]
**First the pieces:**
\[
\frac{\partial z}{\partial x} = \quad \frac{\partial z}{\partial y} =
\]
\[
\frac{\partial x}{\partial s} = \quad \frac{\partial x}{\partial t} =
\]
\[
\frac{\partial y}{\partial s} = \quad \frac{\partial y}{\partial t} =
\]
**And putting it all together:**
\[
\frac{\partial z}{\partial s} =
\]
\[
\frac{\partial z}{\partial t} =
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18fe6d10-65c6-4dea-a463-83c487832ab0%2F33f9a88e-7b79-4d52-98f9-e33e20787db4%2Fupfchj_processed.png&w=3840&q=75)
Transcribed Image Text:Use the chain rule to find \(\frac{\partial z}{\partial s}\) and \(\frac{\partial z}{\partial t}\), where
\[ z = x^2 + xy + y^2, \quad x = 10s + 6t, \quad y = 3s + 6t \]
**First the pieces:**
\[
\frac{\partial z}{\partial x} = \quad \frac{\partial z}{\partial y} =
\]
\[
\frac{\partial x}{\partial s} = \quad \frac{\partial x}{\partial t} =
\]
\[
\frac{\partial y}{\partial s} = \quad \frac{\partial y}{\partial t} =
\]
**And putting it all together:**
\[
\frac{\partial z}{\partial s} =
\]
\[
\frac{\partial z}{\partial t} =
\]
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