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5) For the function f(x, y) = x ln(x y²) and g(x, y) = √√x² + y2, answer the following: a. For f(x, y), find: i. dz ax ii. fy(1, 1) iii. dx dy (do not simplify)

5) For the function f(x, y) = x ln(x y²) and g(x, y) = √√x² + y2, answer the following: a. For f(x, y), find: i. dz ax ii. fy(1, 1) iii. dx dy (do not simplify)

Advanced Engineering Mathematics
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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Solve part a for this
5) For the function f(x, y) = x ln(x y2) and g(x, y) = √² + y², answer the following: a. For f(x, y), find: i. dz ax ii. fy(1, 1) iii. dx dy (do not simplify) b. Find the directional derivative of f(x, y) at the point (1, 1) in the direction = (-4, 3). In what direction (express as a vector) from (1, 1) should you head in order to move in the direction of steepest ascent? In which direction from (1, 1) should you head in order for f(x, y) to not change? i) If 7(t) = (, ³), consider g(()); use the Chain Rule to find f' (t). C. ii) If x and y are both functions of u and v, such that x(u, v) = u²v and y(u, v) = u +3v³, use the Chain az Rule to find at the point where u = 1, v= 1. Draw a "tree diagram" for this problem. du
Transcribed Image Text:5) For the function f(x, y) = x ln(x y2) and g(x, y) = √² + y², answer the following: a. For f(x, y), find: i. dz ax ii. fy(1, 1) iii. dx dy (do not simplify) b. Find the directional derivative of f(x, y) at the point (1, 1) in the direction = (-4, 3). In what direction (express as a vector) from (1, 1) should you head in order to move in the direction of steepest ascent? In which direction from (1, 1) should you head in order for f(x, y) to not change? i) If 7(t) = (, ³), consider g(()); use the Chain Rule to find f' (t). C. ii) If x and y are both functions of u and v, such that x(u, v) = u²v and y(u, v) = u +3v³, use the Chain az Rule to find at the point where u = 1, v= 1. Draw a "tree diagram" for this problem. du
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