(a) Given that f'(x) = V3x² + 1, g(x) = sin(x²) + 1. Let F(x) = f(g(x)). What is F' (x)? (b) Given z = f(x, y), x = x(u, v), y = y(u, v), with x(5, 4) = 3, y(5,4) = 5. %3D Calculate z,(3, 5). You may need to use some of the following values. fx(3, 5) = 1, fx(5, 4) = –1, fy(3,5) = -2, fy(5, 4) = 2, xµ(5, 4) = -3, Xv(5, 4) = -3, Yu(5, 4) = 4, y,(5, 4) = -4.
(a) Given that f'(x) = V3x² + 1, g(x) = sin(x²) + 1. Let F(x) = f(g(x)). What is F' (x)? (b) Given z = f(x, y), x = x(u, v), y = y(u, v), with x(5, 4) = 3, y(5,4) = 5. %3D Calculate z,(3, 5). You may need to use some of the following values. fx(3, 5) = 1, fx(5, 4) = –1, fy(3,5) = -2, fy(5, 4) = 2, xµ(5, 4) = -3, Xv(5, 4) = -3, Yu(5, 4) = 4, y,(5, 4) = -4.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(a) Given that f'(x) = V3x² + 1, g(x) = sin(x²) + 1. Let F(x) = f(g(x)). What is F' (x)?
(b) Given z =
f(x, y), x = x(u, v), y = y(u, v), with x(5, 4) = 3, y(5,4) = 5.
%3D
Calculate z,(3, 5). You may need to use some of the following values.
fx(3, 5) = 1, fx(5, 4) = –1, fy(3,5) = -2, fy(5, 4) = 2, xµ(5, 4) = –3, X»(5, 4) = –3,
Уa(5, 4) 3D 4, У» (5, 4) 3D —4.
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