Explanation 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: The function y = f ( g ( x ) ) , let u = g ( x ) , then y = f ( u ) and d y d x = d y d u ⋅ d u d x . Calculation: The given multivariable function is f ( x , y ) = 4 e 3 x + 2 y . 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 ( 4 e 3 x + 2 y ) = 4 ∂ ∂ x ( e 3 x e 2 y ) = 4 e 2 y ∂ ∂ x ( e 3 x ) = 4 e 2 y [ d d ( 3 x ) ( e 3 x ) ( d d x ( 3 x ) ) ] [ by Chain Rule ] Simplify further and obtain the Partial derivatives, f x ( x , y ) = 4 e 2 y [ e 3 x ( 3 ) ] = 12 e 3 x + 2 y Therefore, the partial derivative with respect x is, f x ( x , y ) = 12 e 3 x + 2 y

Finite Mathematics and Calculus with Applications Books a la Carte Plus MyLab Math Package (10th Edition)

10th Edition

ISBN: 9780133935592

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

Publisher: PEARSON

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Chapter 17.2, Problem 8E

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

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Chapter 17.2, Problem 7E

Chapter 17.2, Problem 9E

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Chapter 17 Solutions

Finite Mathematics and Calculus with Applications Books a la Carte Plus MyLab Math Package (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. 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The partial derivatives f x ( x , y ) , f y ( x , y ) , and the functional values f x ( 2 , − 1 ) and f y ( − 4 , 3 ) .

Solution Summary: The author explains the partial derivatives of f with respect to x and y, and the functional values.

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

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Chapter 17 Solutions