Let f(x, y, z) = x³y³ + z³ and x = s4, y = st², and z = s¹t. (a) Calculate the primary derivatives dx' dy' dz

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) = x³y² + z³ and x = s4, y = st², and z = sªt.
(a) Calculate the primary derivatives
af af af
dx' dy'dz'
Transcribed Image Text:Let f(x, y, z) = x³y² + z³ and x = s4, y = st², and z = sªt. (a) Calculate the primary derivatives af af af dx' dy'dz'
?х ду дz
(b) Calculate ds' ds ds
(Use symbolic notation and fractions where needed.)
дх
əs
ду
дл
дz
Əs
||
=
||
(c) Compute using the Chain Rule.
of ?х
?х дя
of
дл
=
+
дf ду
ду дя
of dz
дz дя
Transcribed Image Text:?х ду дz (b) Calculate ds' ds ds (Use symbolic notation and fractions where needed.) дх əs ду дл дz Əs || = || (c) Compute using the Chain Rule. of ?х ?х дя of дл = + дf ду ду дя of dz дz дя
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