(a) Explanation Given: The function is g ( x , y ) = 8 x + 6 x 2 y + 2 y 2 . Definition used: Partial derivatives : “Let z = f ( x , y ) be a function of two independent variables and let all indicated limits exist. Then, the partial derivative of f with respect to x is ∂ z ∂ x = lim h → 0 f ( x + h , y ) − f ( x , y ) h and the partial derivative of f with respect to y is ∂ z ∂ y = lim h → 0 f ( x , y + h ) − f ( x , y ) h . If the indicated limit does not exist, then the partial derivatives do not exist”. Calculation: The given multivariable function g ( x , y ) = 8 x + 6 x 2 y + 2 y 2 . Use the definition of the partial derivative and compute the partial derivatives with respect to x , ∂ g ∂ x = lim h → 0 g ( x + h , y ) − g ( x , y ) h = lim h → 0 [ 8 ( x + h ) + 6 ( x + h ) 2 y + 2 y 2 ] − [ 8 x + 6 x 2 y + 2 y 2 ] h (b) To determine To find: The partial derivative with respect to y ∂ g ∂ y . (c) To determine To find: The value of ∂ z ∂ y ( − 3 , 0 ) . (d) To determine To find: The value of g x ( 2 , 1 ) .

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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Question

Chapter 17.2, Problem 2E

(a)

To determine

To find: The partial derivative with respect to x ∂g∂x .

(b)

To determine

To find: The partial derivative with respect to y ∂g∂y .

(c)

To determine

To find: The value of ∂z∂y(−3,0) .

(d)

To determine

To find: The value of gx(2,1) .

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Chapter 17.2, Problem 1E

Chapter 17.2, Problem 3E

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