Explanation Given: An algebraic function is; f ( x , y ) = 4 x 3 y 2 − 4 x y Formula used: The formula of derivative is; d d x ( x n ) = n x n − 1 Calculation: Consider the function: f ( x , y ) = 4 x 3 y 2 − 4 x y Take second order partial derivative of the function with respect to x as mentioned below, f x = ∂ ∂ x ( 4 x 3 y 2 − 4 x y ) = 12 x 2 y 2 − 4 y Further, differentiate partially with respect to x as; f x x = ∂ ∂ x ( f x ) = ∂ ∂ x ( 12 x 2 y 2 − 4 y ) f x x = 24 x y 2 Now calculate first order partial derivative of the function with respect to x and then calculate the second order partial derivative with respect to y

11th Edition

ISBN: 8220101336323

Author: MULLINS

Publisher: PEARSON

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Chapter 14, Problem 27RE

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To Calculate: The second order derivatives (fxx,fxy) of the function f(x,y)=4x3y2−4xy.

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Chapter 14, Problem 26RE

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Chapter 14 Solutions

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The second order derivatives ( f x x , f x y ) of the function f ( x , y ) = 4 x 3 y 2 − 4 x y .

Solution Summary: The author explains the second order derivatives of the function f(x,y)=4x3y

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To Calculate: The second order derivatives (fxx,fxy) of the function f(x,y)=4x3y2−4xy.

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Chapter 14 Solutions