Explanation Given information: The function is f ( s , t ) = t sin s t . Explanation: The partial derivative of the function f ( s , t ) with respect to s is the derivative of the function f ( s , t ) with respect to s treating t as a constant. Therefore, ∂ f ∂ s = ∂ ∂ s ( t sin s t ) = t ∂ ( sin s t ) ∂ s By using chain rule, ∂ f ∂ s = t cos s t ∂ ( s t ) ∂ s = t cos s t × t = t 2 cos s t ⇒ ∂ f ∂ s = t 2 cos s t . Similarly, the partial derivative of the function f ( s , t ) with respect to t is the derivative of the function f ( s , t ) with respect to t treating s as a constant

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 8, Problem 47RE

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The partial derivatives ∂f∂s and ∂f∂t, where the function is f(s,t)=tsinst.

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Chapter 8, Problem 46RE

Chapter 8, Problem 48RE

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Calculus & Its Applications (14th Edition)

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The partial derivatives ∂ f ∂ s and ∂ f ∂ t , where the function is f ( s , t ) = t sin s t .

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The partial derivatives ∂f∂s and ∂f∂t, where the function is f(s,t)=tsinst.

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Chapter 8 Solutions