Let f(x, y, z) = xy³ + z and x = st³, y = st³, and z = = s²t². (a) Calculate the primary derivatives af əx af ду af əz ду მs || (b) Calculate Əx Əs дz Əs || || || || || (c) Use the Chain Rule to compute af Əs In (c) express your answer in terms of the independent variables t, s =

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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Let f(x, y, z) = xy³ + z and x = = st³, y = st³, and z =
= s²t².
(a) Calculate the primary derivatives
af
?x
af
ду
af
əz
?x
Əs
(b) Calculate
ду
Əs
||
əz
მs
|| ||
||
||
||
(c) Use the Chain Rule to compute
af
Əs
In (c) express your answer in terms of the independent variables t, s
=
Transcribed Image Text:Let f(x, y, z) = xy³ + z and x = = st³, y = st³, and z = = s²t². (a) Calculate the primary derivatives af ?x af ду af əz ?x Əs (b) Calculate ду Əs || əz მs || || || || || (c) Use the Chain Rule to compute af Əs In (c) express your answer in terms of the independent variables t, s =
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