Explanation Given: The function is g ( x , y ) = x 2 + y 2 + 1 , P ( 1 , 2 ) , Q ( 2 , 3 ) . Formula used: Gradient is given by, ∇ f ( x , y ) = f x ( x , y ) i + f y ( x , y ) j Directional derivative is given by, D u f ( x , y ) = ∇ f ( x , y ) ⋅ u Calculation: Partial differentiate g ( x , y ) with respect to y , g y ( x , y ) = 2 y which is continuous. Now partial differentiate g ( x , y ) with respect to x , g x ( x , y ) = 2 x which is continuous. Gradient is given by, ∇ f ( x , y ) = f x ( x , y ) i + f y ( x , y ) j Now put, x = 1

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ISBN: 9781285057095

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 13.6, Problem 23E

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To calculate: For the function g(x,y)=x2+y2+1, P(1,2), Q(2,3). Find the directional derivative of the given function at P in the direction of PQ⇀.

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Chapter 13.6, Problem 22E

Chapter 13.6, Problem 24E

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For the function g ( x , y ) = x 2 + y 2 + 1 , P ( 1 , 2 ) , Q ( 2 , 3 ) . Find the directional derivative of the given function at P in the direction of P Q ⇀ .

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To calculate: For the function g(x,y)=x2+y2+1, P(1,2), Q(2,3). Find the directional derivative of the given function at P in the direction of PQ⇀.

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Chapter 13 Solutions