Question 9 Chain Rule (Multiple independent variables) ♥ Given z=x³ + xy¹, x= uv³+w5, y =u+ve² Əz dv then find: when u = 1, v= −1, w = 0 Question Help: Video Submit Question
Question 9 Chain Rule (Multiple independent variables) ♥ Given z=x³ + xy¹, x= uv³+w5, y =u+ve² Əz dv then find: when u = 1, v= −1, w = 0 Question Help: Video Submit Question
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 9**
**Chain Rule (Multiple independent variables)**
Given:
\[ z = x^3 + xy^4, \quad x = uw^3 + w^5, \quad y = u + ve^w \]
Then find: \(\frac{\partial z}{\partial v}\) when \( u = 1, \, v = -1, \, w = 0 \)
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This question involves using the chain rule for functions with multiple independent variables to find the partial derivative of \( z \) with respect to \( v \). The expressions for \( x \) and \( y \) are given in terms of \( u \), \( v \), and \( w \). You need to use these expressions to calculate the desired derivative.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a3f3121-07ef-4e2d-8122-d3ccd0e5a601%2Fed049ea3-68df-40da-9805-6c2adccfbdb6%2Fp6telff_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 9**
**Chain Rule (Multiple independent variables)**
Given:
\[ z = x^3 + xy^4, \quad x = uw^3 + w^5, \quad y = u + ve^w \]
Then find: \(\frac{\partial z}{\partial v}\) when \( u = 1, \, v = -1, \, w = 0 \)
---
**Question Help:** [Video]
**Submit Question**
---
This question involves using the chain rule for functions with multiple independent variables to find the partial derivative of \( z \) with respect to \( v \). The expressions for \( x \) and \( y \) are given in terms of \( u \), \( v \), and \( w \). You need to use these expressions to calculate the desired derivative.
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