To determine The partial derivatives ∂ y ∂ x and ∂ y ∂ t of the function y . Explanation It is given that the function y is sin ( π x ) sin ( π t 2 ) which represents the displacement of a wave in a string where x is the position and t is the time. Here, the dependent variable is y and the independent variables are x and t. Differentiate y = sin ( π x ) sin ( π t 2 ) partially with respect to x as follows. ∂ y ∂ x = ∂ ∂ x ( sin ( π x ) sin ( π t 2 ) ) = sin ( π t 2 ) ∂ ∂ x ( sin ( π x ) ) = sin ( π t 2 ) cos ( π x ) ∂ ∂ x ( π x ) = sin ( π t 2 ) cos ( π x ) ( π ) That is, ∂ y ∂ x = π sin ( π t 2 ) cos ( π x ) . Thus, the partial derivative of y = sin ( π x ) sin ( π t 2 ) with respect to r is π sin ( π t 2 ) cos ( π x ) . Differentiate y = sin ( π x ) sin ( π t 2 ) partially with respect to t 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 37E

To determine

The partial derivatives ∂y∂x and ∂y∂t of the function y.

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Chapter 29.3, Problem 36E

Chapter 29.3, Problem 38E

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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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