Explanation Given: The function is f ( x , y ) = sin 2 x cos y , P ( π , 0 ) , Q ( π 2 , π ) . Formula used: Directional derivative is given by, D u f ( x , y ) = f x ( x , y ) cos θ + f y ( x , y ) sin θ Calculation: Partial differentiate f ( x , y ) with respect to y , f y ( x , y ) = cos 2 x ⋅ ( 0 ) cos y + sin 2 x ( − sin y ) = − sin 2 x sin y which is continuous. Partial differentiate f ( x , y ) with respect to x , f x ( x , y ) = 2 cos 2 x cos y + sin 2 x ( − sin y ) ( 0 ) = 2 cos 2 x cos y which is continuous. Vector in the specified direction is, P Q ⇀ = ( π 2 − π ) i + ( π − 0 ) j = − π 2 i+ π j Unit vector u = v ‖ v ‖ = − π 2 i+ π j ( − π 2 ) 2 + <

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ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Question

Chapter 13.6, Problem 14E

To determine

To calculate: For the given function f(x,y)=sin2xcosy at P(π,0) in the direction of PQ⇀.

the directional derivative

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Chapter 13.6, Problem 13E

Chapter 13.6, Problem 15E

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For the given function f ( x , y ) = sin 2 x cos y at P ( π , 0 ) in the direction of P Q ⇀ . the directional derivative

Solution Summary: The author explains the directional derivative of f(x,y)=mathrmsin2x

Concept explainers

To calculate: For the given function f(x,y)=sin2xcosy at P(π,0) in the direction of PQ⇀.

the directional derivative

Want to see the full answer?

Chapter 13 Solutions

For the given function f ( x , y ) = sin 2 x cos y at P ( π , 0 ) in the direction of P Q ⇀ . the directional derivative

Solution Summary: The author explains the directional derivative of f(x,y)=mathrmsin2x

Concept explainers

To calculate: For the given function f(x,y)=sin2xcosy at P(π,0) in the direction of PQ⇀. the directional derivative

Want to see the full answer?

Chapter 13 Solutions

To calculate: For the given function f(x,y)=sin2xcosy at P(π,0) in the direction of PQ⇀.

the directional derivative