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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A tank holds a 135 gal solution of water and salt. Initially, the solution contains 21 lb of salt. A salt solution with a concentration of 3 lb of salt per gal begins flowing into the tank at the rate of 3 gal per minute. The solution in the tank also begins flowing out at a rate of 3 gal per minute. Let y be the amount of salt present in the tank at time t. (a) Find an expression for the amount of salt in the tank at any time. (b) How much salt is present after 51 minutes? (c) As time increases, what happens to the salt concentration?

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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)