Explanation Given: The function f ( x , y ) = 3 x 2 y 4 + 6 x 2 − 7 y 2 . That is, z = 3 x 2 y 4 + 6 x 2 − 7 y 2 ... ( 1 ) . Approach: The value of d z is determined by the differentiating the function with respect to x and y . Calculation: The d z value is calculated as, Partial differentiation of the equation (1) with respect to x . ∂ z ∂ x = ∂ ∂ x ( 3 x 2 y 4 + 6 x 2 − 7 y 2 ) ∂ z ∂ x = ∂ ∂ x ( 3 x 2 y 4 ) + ∂ ∂ x ( 6 x 2 − 7 y 2 ) ∂ z ∂ x = 6 x y 4 + 6 1 2 x 2 − 7 y 2 ⋅ 2 x ∂ z ∂ x = 6 x y 4 + 6 x x 2 − 7 y 2 ... ( 2 ) Partial differentiation of the equation (1) with respect to y . ∂ z ∂ y = ∂ ∂ y ( 3 x 2 y 4 + 6 x 2 − 7 y 2 ) ∂ z ∂ y = ∂ ∂ y ( 3 x 2 y 4 ) + ∂ ∂ y ( 6 x 2 − 7 y 2 ) ∂ z ∂ y = 12 x 2 y 3 + 6 1 2 x 2 − 7 y 2 ⋅ ( − 14 y ) ∂ z ∂ y = 12 x 2 y 3 − 42 y x 2 − 7 y 2 To determine (b) To find: The value of the d z for the function 3 x 2 y 4 + 6 x 2 − 7 y 2 .

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

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Chapter 9.4, Problem 1YT

To determine

(a)

To find:

The value of the dz for the function 3x2y4+6x2−7y2.

To determine

(b)

To find:

The value of the dz for the function 3x2y4+6x2−7y2.

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Chapter 9.3, Problem 41E

Chapter 9.4, Problem 2YT

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Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

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