Let f(x, y, z) = x*y+ z* and x = st², y = st, and z = s²t. (a) Calculate the primary derivatives se dx se dz (b) Calculate dx ds ду dz ds (c) Use the Chain Rule to compute af ds In (c) express your answer in terms of the independent variables t, s I| || || I| ||

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 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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Let f(x, y, z) = x*y+ z* and x =
st, y = st, and z =
(a) Calculate the primary derivatives
af
dx
af
%3D
ду
af
dz
(b) Calculate
dx
ds
dz
ds
(c) Use the Chain Rule to compute
af
ds
In (c) express your answer in terms of the independent variables t, s
II
Transcribed Image Text:Let f(x, y, z) = x*y+ z* and x = st, y = st, and z = (a) Calculate the primary derivatives af dx af %3D ду af dz (b) Calculate dx ds dz ds (c) Use the Chain Rule to compute af ds In (c) express your answer in terms of the independent variables t, s II
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