43. Find the first partial derivatives f(x, t) = e-t sin(x) g(x, y) X (x + y)² h(x, y) = tan ¹(y/x)
43. Find the first partial derivatives f(x, t) = e-t sin(x) g(x, y) X (x + y)² h(x, y) = tan ¹(y/x)
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 43 please
![### Partial Derivatives Exercise
**Problem 43:** Find the first partial derivatives
Given functions:
\[ f(x, t) = e^{-t} \sin(\pi x) \]
\[ g(x, y) = \frac{x}{(x + y)^2} \]
\[ h(x, y) = \tan^{-1}(y/x) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb24b717-8ee5-4ca9-8061-74ddb7e91c1a%2F7bdcdba6-4e94-4714-bceb-d4f9a09514a7%2Fhstimws_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Partial Derivatives Exercise
**Problem 43:** Find the first partial derivatives
Given functions:
\[ f(x, t) = e^{-t} \sin(\pi x) \]
\[ g(x, y) = \frac{x}{(x + y)^2} \]
\[ h(x, y) = \tan^{-1}(y/x) \]
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Step 1: Find the first partial derivative of the given functions
VIEWStep 2: Find the first partial derivative for part(a)
VIEWStep 3: Differentiate equation (2) partially with respect to x
VIEWStep 4: Again differentiate equation (2) partially with respect to y
VIEWStep 5: Differentiate equation (3) partially with respect to y
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