Explanation Given: y = cos sin ( tan π 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 sin x = cos x , d d x cos x = − sin x d d x tan x = sec 2 x d d x x n = n x n − 1 Calculation: To find derivative of the function y = cos sin ( tan π x ) Differentiate both side of the equation with respect to x as d y d x = d d x [ cos sin ( tan π x ) ] Now use chain rule of differentiation to solve it further, as y ′ = d d x [ cos sin ( tan π x ) ] = − sin sin ( tan π x ) d d x ( sin ( tan π x ) ) 1 / 2 = − sin sin ( tan π x )

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Chapter 3.8, Problem 35E

To determine

To find derivative of the function

y=cossin(tanπx)

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Chapter 3.8, Problem 34E

Chapter 3.8, Problem 36E

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Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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To find derivative of the function y = cos sin ( tan π x )

Solution Summary: The author explains how to find derivative of the function y=mathrmcossqrt

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To find derivative of the function y=cossin(tanπx)

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Chapter 3 Solutions

To find derivative of the function

y=cossin(tanπx)