1. Obtain the directional derivative of: a.. f(x,y) = x²-4x³y² at the point (1,-2) in the direction of a unit vector whose angle with the semi-axis x is 1, u = cos i + sen j b. f(x,y) = x²-xy + 3y² at the point (-1,-2) in the direction of a unit vector whose angle with the semi-axis x is u = cos 0 i+sen j c. f(x,y) = x²sin y at the point (1.1) in the direction of a vector v = 3i-4j
1. Obtain the directional derivative of: a.. f(x,y) = x²-4x³y² at the point (1,-2) in the direction of a unit vector whose angle with the semi-axis x is 1, u = cos i + sen j b. f(x,y) = x²-xy + 3y² at the point (-1,-2) in the direction of a unit vector whose angle with the semi-axis x is u = cos 0 i+sen j c. f(x,y) = x²sin y at the point (1.1) in the direction of a vector v = 3i-4j
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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![1. Obtain the directional derivative of:
a.. f(x,y) = x²-4x³y² at the point (1,-2) in the direction of a unit vector whose
angle with the semi-axis x is 1, u = cos i + sen j
b. f(x,y) = x²-xy + 3y² at the point (-1,-2) in the direction of a unit vector whose
angle with the semi-axis x is u = cos 0 i+sen j
c. f(x,y) = x²sin y at the point (1.1) in the direction of a vector v = 3i-4j](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ffc800b-abe3-4396-949c-2dda6c946b8d%2F68cd3f9a-b865-47e3-a778-c9b580ca1fb0%2Fswa51r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Obtain the directional derivative of:
a.. f(x,y) = x²-4x³y² at the point (1,-2) in the direction of a unit vector whose
angle with the semi-axis x is 1, u = cos i + sen j
b. f(x,y) = x²-xy + 3y² at the point (-1,-2) in the direction of a unit vector whose
angle with the semi-axis x is u = cos 0 i+sen j
c. f(x,y) = x²sin y at the point (1.1) in the direction of a vector v = 3i-4j
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