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Əs 2. If st", find 2 and 3. = ди

Əs 2. If st", find 2 and 3. = ди

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem 2:** If \( s = t^u \), find \(\frac{\partial s}{\partial u}\) and \(\frac{\partial s}{\partial t}\). **Explanation:** This problem involves finding partial derivatives of the function \( s = t^u \) with respect to the variables \( u \) and \( t \). - **Partial Derivative with respect to \( u \) (\(\frac{\partial s}{\partial u}\)):** To find this derivative, consider \( t \) as a constant and differentiate with respect to \( u \). The result involves the natural logarithm of \( t \). - **Partial Derivative with respect to \( t \) (\(\frac{\partial s}{\partial t}\)):** For this derivative, treat \( u \) as a constant and differentiate \( s \) with respect to \( t \). Utilizing these differentiation techniques helps in applications involving variables with interdependencies.
Transcribed Image Text:**Problem 2:** If \( s = t^u \), find \(\frac{\partial s}{\partial u}\) and \(\frac{\partial s}{\partial t}\). **Explanation:** This problem involves finding partial derivatives of the function \( s = t^u \) with respect to the variables \( u \) and \( t \). - **Partial Derivative with respect to \( u \) (\(\frac{\partial s}{\partial u}\)):** To find this derivative, consider \( t \) as a constant and differentiate with respect to \( u \). The result involves the natural logarithm of \( t \). - **Partial Derivative with respect to \( t \) (\(\frac{\partial s}{\partial t}\)):** For this derivative, treat \( u \) as a constant and differentiate \( s \) with respect to \( t \). Utilizing these differentiation techniques helps in applications involving variables with interdependencies.
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