Explanation Given: y = cos ( e tan 3 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 cos x = − sin x , d d x ( tan x ) = sec 2 x Power rule of differentiation formula d d x x n = n x n − 1 Calculation: To calculate y ′ , where y = cos ( e tan 3 x ) Differentiate both side of the equation with respect to x as y ′ = d d x [ cos ( e tan 3 x ) ] Now use chain rule of differentiation to solve it further, as y ′ = d d x [ cos ( e tan 3 x ) ] = ( − sin ( e tan 3 x ) ) d d x ( e tan 3 x ) = −

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Question

Chapter 3, Problem 49E

To determine

To calculate y′ , where

y=cos(e tan3x)

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Chapter 3, Problem 48E

Chapter 3, Problem 50E

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Chapter 3 Solutions

Biocalculus

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Knowledge Booster

To calculate y ′ , where y = cos ( e tan 3 x )

Solution Summary: The author calculates yprime, where y=mathrmcos(esqrt

To calculate y′ , where y=cos(e tan3x)

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Chapter 3 Solutions

To calculate y′ , where

y=cos(e tan3x)