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
icon
Related questions
Question
**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.
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.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,