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4.(2.5) Let g(x, y) = (x² + x, y + 3) and f(u, v) = (u - v, u² + v²). (1) Find Df(u, v) and Dg(x, y). (2) Find g(1, 1), Dg(1, 1) and D(f ○ g)(1, 1).

4.(2.5) Let g(x, y) = (x² + x, y + 3) and f(u, v) = (u - v, u² + v²). (1) Find Df(u, v) and Dg(x, y). (2) Find g(1, 1), Dg(1, 1) and D(f ○ g)(1, 1).

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 22E: Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and...
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4.(2.5) Let g(x, y) = (x² + x, y + 3) and f(u, v) = (u – v, u² + v²). (1) Find Df(u, v) and Dg(x, y). (2) Find g(1, 1), Dg(1, 1) and D(f ○ g)(1, 1). 5.(2.6) (1) Let f(x, y) = ln(x² + y³) and v = derivative of f in the direction of v at x0 = (0, 1). Find Vf(x, y) and the directional 2 (2) Consider a curve given by x² - 2xy + y³ = 1. Find a normal vector to the curve at x0 = (2,1).
Transcribed Image Text:4.(2.5) Let g(x, y) = (x² + x, y + 3) and f(u, v) = (u – v, u² + v²). (1) Find Df(u, v) and Dg(x, y). (2) Find g(1, 1), Dg(1, 1) and D(f ○ g)(1, 1). 5.(2.6) (1) Let f(x, y) = ln(x² + y³) and v = derivative of f in the direction of v at x0 = (0, 1). Find Vf(x, y) and the directional 2 (2) Consider a curve given by x² - 2xy + y³ = 1. Find a normal vector to the curve at x0 = (2,1).
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