To determine The partial derivatives of the function, ∂ z ∂ x and ∂ z ∂ y . Explanation Given that the function is z = 4 x 2 + x sin y . Here, the dependent variable is z and the independent variables are x and y . Differentiate z partially with respect to x as follows. ∂ z ∂ x = ∂ ∂ x ( 4 x 2 + x sin y ) = ∂ ∂ x ( 4 x 2 ) + ∂ ∂ x ( x sin y ) = 4 ( 2 x ) + sin y ∂ ∂ x ( x ) + x ∂ ∂ x ( sin y ) use product rule = 8 x + sin y ( 1 ) + x ⋅ 0 That is, ∂ z ∂ x = 8 x + sin y . Thus, the partial derivative of z with respect to x is 8 x + sin y . Differentiate z partially with respect to y as follows

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 29.3, Problem 1PE

To determine

The partial derivatives of the function, ∂z∂x and ∂z∂y.

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Chapter 29.2, Problem 46E

Chapter 29.3, Problem 2PE

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Given the cubic function f(x) = x^3-6x^2 + 11x- 6, do the following: Plot the graph of the function. Find the critical points and determine whether each is a local minimum, local maximum, or a saddle point. Find the inflection point(s) (if any).Identify the intervals where the function is increasing and decreasing. Determine the end behavior of the graph.

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Chapter 29 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 29.1 - Practice Exercise If f(x, y) = 4xy2 – 3x2y, find...Ch. 29.1 - Prob. 1E Ch. 29.1 - Prob. 2E Ch. 29.1 - Prob. 3E Ch. 29.1 - Prob. 4E Ch. 29.1 - Prob. 5E Ch. 29.1 - Prob. 6E Ch. 29.1 - Prob. 7E Ch. 29.1 - Prob. 8E Ch. 29.1 - Prob. 9E

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