Assume that z = f(w), w = g(x,y), x=4r³-s², and y = re. If g (4,1)=-4, g,(4,1)=2, f'(7)= -2, and g(4,1)= 7, find the following dz dz and dr r=1,s=0 dsr=1, s=0 dz dz and or r=1,s=0 dsr=1,s=0 Calculate dz dr
Assume that z = f(w), w = g(x,y), x=4r³-s², and y = re. If g (4,1)=-4, g,(4,1)=2, f'(7)= -2, and g(4,1)= 7, find the following dz dz and dr r=1,s=0 dsr=1, s=0 dz dz and or r=1,s=0 dsr=1,s=0 Calculate dz dr
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Problem Statement:
Assume that \( z = f(w), w = g(x, y) \), \( x = 4r^3 - s^2 \), and \( y = re^s \).
If \( g_x(4,1) = -4 \), \( g_y(4,1) = 2 \), \( f'(7) = -2 \), and \( g(4, 1) = 7 \), find the following:
\[
\left. \frac{\partial z}{\partial r} \right|_{r=1, s=0} \quad \text{and} \quad \left. \frac{\partial z}{\partial s} \right|_{r=1, s=0}
\]
### Calculation:
Calculate
\[
\left. \frac{\partial z}{\partial r} \right|_{r=1, s=0} \quad \text{and} \quad \left. \frac{\partial z}{\partial s} \right|_{r=1, s=0}
\]
\[
\left. \frac{\partial z}{\partial r} \right|_{r=1, s=0} = \boxed{}
\]
\[
\left. \frac{\partial z}{\partial s} \right|_{r=1, s=0} = \boxed{}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41a1af84-f79e-495e-9bf6-e155c46aa5b8%2Fe7f0b93d-1422-4505-b806-fbb8c7ea0f52%2Fioawgzf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
Assume that \( z = f(w), w = g(x, y) \), \( x = 4r^3 - s^2 \), and \( y = re^s \).
If \( g_x(4,1) = -4 \), \( g_y(4,1) = 2 \), \( f'(7) = -2 \), and \( g(4, 1) = 7 \), find the following:
\[
\left. \frac{\partial z}{\partial r} \right|_{r=1, s=0} \quad \text{and} \quad \left. \frac{\partial z}{\partial s} \right|_{r=1, s=0}
\]
### Calculation:
Calculate
\[
\left. \frac{\partial z}{\partial r} \right|_{r=1, s=0} \quad \text{and} \quad \left. \frac{\partial z}{\partial s} \right|_{r=1, s=0}
\]
\[
\left. \frac{\partial z}{\partial r} \right|_{r=1, s=0} = \boxed{}
\]
\[
\left. \frac{\partial z}{\partial s} \right|_{r=1, s=0} = \boxed{}
\]
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