Explanation Given: The function is f ( x , y ) = ln | 4 x 4 − 2 x 2 y 2 | . Definition used: Partial derivatives : “The partial derivative of f with respect to x is the derivative of f obtained by treating x as a variable and y as a constant. The partial derivative of f with respect to y is the derivative of f obtained by treating y as a variable and x as a constant”. Formula used: 1. Power Rule: If n is real number, then d d x ( x n ) = n x n − 1 . 2. Chain Rule: If the function y = f ( g ( x ) ) , then d y d x = d y d u ⋅ d u d x . Where u = g ( x ) , y = f ( u ) . Calculation: Treat y as a constant and x as a variable to find the Partial derivative of the function f ( x , y ) with respect to x , f x ( x , y ) = ∂ ∂ x ( ln | 4 x 4 − 2 x 2 y 2 | ) = ∂ ∂ ( 4 x 4 − 2 x 2 y 2 ) ( ln | 4 x 4 − 2 x 2 y 2 | ) ∂ ∂ x ( 4 x 4 − 2 x 2 y 2 ) [ by Chain Rule ] = 1 4 x 4 − 2 x 2 y 2 ( ∂ ∂ x ( 4 x 4 ) − ∂ ∂ x ( 2 x 2 y 2 ) ) = 1 4 x 4 − 2 x 2 y 2 ( 16 x 3 − 2 y 2 ∂ ∂ x ( x 2 ) ) On further simplifications, f x ( x , y ) = 1 4 x 4 − 2 x 2 y 2 ( 16 x 3 − 2 y 2 ( 2 x ) ) = 1 4 x 4 − 2 x 2 y 2 ( 16 x 3 − 4 x y 2 ) = 8 x 2 − 2 y 2 2 x 3 − x y 2 Therefore, the partial derivative with respect x is, f x ( x , y ) = 8 x 2 − 2 y 2 2 x 3 − x y 2

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 17.2, Problem 14E

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To find: The partial derivatives fx(x,y) , fy(x,y) and fx(2,−1) , fy(−4,3) .

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Chapter 17.2, Problem 13E

Chapter 17.2, Problem 15E

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Chapter 17 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

Ch. 17.1 - For the function in Example 1, find f(2, 3)....Ch. 17.1 - Prob. 2YT Ch. 17.1 - Prob. 3YT Ch. 17.1 - Prob. 4YT Ch. 17.1 - Prob. 1WE Ch. 17.1 - Prob. 2WE Ch. 17.1 - Prob. 3WE Ch. 17.1 - Prob. 4WE Ch. 17.1 - Prob. 5WE Ch. 17.1 - Prob. 6WE

Ch. 17.1 - Let f(x, y) = 2x 3y + 5. Find the following....Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E Ch. 17.1 - Prob. 7E Ch. 17.1 - Prob. 8E Ch. 17.1 - Graph the first-octant portion of each plane. 9.2x...Ch. 17.1 - Prob. 10E Ch. 17.1 - Prob. 11E Ch. 17.1 - Prob. 12E Ch. 17.1 - Prob. 13E Ch. 17.1 - Prob. 14E Ch. 17.1 - Prob. 15E Ch. 17.1 - Prob. 16E Ch. 17.1 - Prob. 17E Ch. 17.1 - Prob. 18E Ch. 17.1 - Prob. 19E Ch. 17.1 - Prob. 20E Ch. 17.1 - Prob. 21E Ch. 17.1 - Prob. 22E Ch. 17.1 - Match each equation in Exercises 2328 with its...Ch. 17.1 - Prob. 24E Ch. 17.1 - Prob. 25E Ch. 17.1 - Match each equation in Exercises 2328 with its...Ch. 17.1 - Prob. 27E Ch. 17.1 - Prob. 28E Ch. 17.1 - Prob. 29E Ch. 17.1 - Prob. 30E Ch. 17.1 - Prob. 31E Ch. 17.1 - Prob. 32E Ch. 17.1 - Prob. 33E Ch. 17.1 - Prob. 34E Ch. 17.1 - Production Find the level curve at a production of...Ch. 17.1 - Prob. 36E Ch. 17.1 - Prob. 37E Ch. 17.1 - Individual Retirement Accounts The multiplier...Ch. 17.1 - 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If the function...Ch. 17 - Prob. 85RE Ch. 17 - Prob. 86RE Ch. 17 - Prob. 87RE Ch. 17 - Prob. 88RE Ch. 17 - Prob. 89RE Ch. 17 - Prob. 90RE Ch. 17 - Prob. 91RE Ch. 17 - Prob. 92RE Ch. 17 - Prob. 93RE Ch. 17 - Prob. 94RE Ch. 17 - Prob. 95RE Ch. 17 - Prob. 96RE Ch. 17 - Profit The total profit from 1 acre of a certain...Ch. 17 - Prob. 98RE Ch. 17 - Prob. 99RE Ch. 17 - Prob. 100RE Ch. 17 - Prob. 101RE Ch. 17 - Prob. 102RE Ch. 17 - Prob. 103RE Ch. 17 - Prob. 104RE Ch. 17 - Prob. 105RE Ch. 17 - Prob. 106RE

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The partial derivatives f x ( x , y ) , f y ( x , y ) and f x ( 2 , − 1 ) , f y ( − 4 , 3 ) .

Solution Summary: The author explains the partial derivatives of f with respect to x and y, and their value at specific points.

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To find: The partial derivatives fx(x,y) , fy(x,y) and fx(2,−1) , fy(−4,3) .

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Chapter 17 Solutions