• ƒ(•) : R² → R² and g(-) : R³ → R² are given by ƒ (») = (37,³² (1²1/2-1/²) 3y₁ + y₂ Find the Jacobians ƒ'(y) and g'(x). For x = (−1 2 1)¹, find g′(§), ƒ' (g(x)), and (ƒog)'(X). Suppose X1 and gx₂= x3 x₁ + x₂ + x3 √x²x₂x3 + x²³

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 28E
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y₁
Suppose f(): R² → R² and g(.) : R³ → R² are given by f
Y2
x1
and gx₂=
x3,
=
3y₁+y/₂.
Find the Jacobians f'(y) and g'(x). For x = (−1 2 1)¹, find g'(x), ƒ'(g(x)), and (ƒog)'(X).
x1 + x₂ + x3
x₁x₂x3 + x²3
Transcribed Image Text:y₁ Suppose f(): R² → R² and g(.) : R³ → R² are given by f Y2 x1 and gx₂= x3, = 3y₁+y/₂. Find the Jacobians f'(y) and g'(x). For x = (−1 2 1)¹, find g'(x), ƒ'(g(x)), and (ƒog)'(X). x1 + x₂ + x3 x₁x₂x3 + x²3
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