Explanation Given: The provided function is f ( x , y ) = 10 y 1 − x . Formula used: If f ( x ) = x n for any number n , then the derivative is defined by the formula, f ′ ( x ) = n x n − 1 Calculation: f x is calculated by treating x as variable and y as a constant and using the formula above. f ( x , y ) = 10 y 1 − x = 10 y ( 1 − x ) − 1 f x = 10 y × ( − 1 ) × ( 1 − x ) − 1 − 1 × ( − 1 ) = 10 y ( 1 − x ) 2 Here f x is the partial derivative of f with respect to x . Calculate f y by treating y as variable and x as a constant and using the formula above. f ( x , y ) = 10 y 1 − x f y = 10 × 1 1 − x = 10 1 − x Here f y is the partial derivative of f with respect to y. Now to find f x x , take the partial derivative of f x with respect to x. f x = 10 y ( 1 − x ) 2 = 10 y ( 1 − x ) − 2 f x x = 10 y × ( − 2 ) × ( 1 − x ) − 2 − 1 × ( − 1 ) f x x = 20 y ( 1 − x ) 3 Here f x x is the partial derivative of f x with respect to x

Mathematics With Applications, Loose-leaf Edition Plus Mylab Math With Pearson Etext -- 18-week Access Card Package (12th Edition)

12th Edition

ISBN: 9780135998304

Author: Margaret L. Lial, Tom Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 14.2, Problem 30E

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To find: All second-order partial derivatives of f(x,y)=10y1−x.

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Chapter 14.2, Problem 29E

Chapter 14.2, Problem 31E

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Mathematics With Applications, Loose-leaf Edition Plus Mylab Math With Pearson Etext -- 18-week Access Card Package (12th Edition)

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All second-order partial derivatives of f ( x , y ) = 10 y 1 − x .

Solution Summary: The author explains the second-order partial derivatives of f(x,y)=10y-x.

To find: All second-order partial derivatives of f(x,y)=10y1−x.

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Chapter 14 Solutions