Let f(x,y) = xy, g(s, t) (2s + 3t, 4s+t), and F(s, t) = (ƒ 0 g)(s, t). Evaluate DF(s, t) both directly and by using the Chain Rule. =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Real Analysis II Q2.
1. Evaluate \( F'(t) \) both directly and by using the Chain Rule.

2. Let \( f(x, y) = xy \), \( g(s, t) = (2s + 3t, 4s + t) \), and \( F(s, t) = (f \circ g)(s, t) \). Evaluate \( DF(s, t) \) both directly and by using the Chain Rule.

3. Let \( f(x, y, z) = xyz \), \( g(s, t) = (3s + st, s, t) \), and \( F(s, t) = (f \circ g)(s, t) \).
Transcribed Image Text:1. Evaluate \( F'(t) \) both directly and by using the Chain Rule. 2. Let \( f(x, y) = xy \), \( g(s, t) = (2s + 3t, 4s + t) \), and \( F(s, t) = (f \circ g)(s, t) \). Evaluate \( DF(s, t) \) both directly and by using the Chain Rule. 3. Let \( f(x, y, z) = xyz \), \( g(s, t) = (3s + st, s, t) \), and \( F(s, t) = (f \circ g)(s, t) \).
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