Explanation Given: The given problem is r ( x ) = e x sin x . Concept Used: Chain rule of differentiation is: d d x f [ g ( x ) ] = d d g f ( g ) d g d x , where u is a differentiable function at x and f is a differentiable function at u ( x ) d d x e x = e x d d x x n = n x n − 1 product rule of differentiation formula d d x ( u v ) = v d d x u + u d d x v Differentiation formula of some trigonometric function d d x ( sin x ) = cos x , d d x ( cos x ) = − sin x Calculation: To find differentiation of function r ( x ) = e x sin x Differentiate both side of the equation with respect to x as r ( x ) = e x sin x d d x ( r ( x ) ) = d d x [ ( sin x ) − 1

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Chapter 3.3, Problem 12PS

To determine

To differentiate r(x)=exsinx .

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Chapter 3.3, Problem 11PS

Chapter 3.3, Problem 13PS

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Chapter 3 Solutions

Student's Solution and Survival Manual for Calculus

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To differentiate r ( x ) = e x sin x .

Solution Summary: The author explains the chain rule of differentiation of a trigonometric function.

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To differentiate r(x)=exsinx .

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Chapter 3 Solutions