Explanation Given information: f ( x ) = sin x and n = 4 m + r where m is a whole number and r = 0 , 1 , 2 or 3 Formula Used: The derivative of the standard trigonometry function: d d x ( sin x ) = cos x and d d x ( cos x ) = − sin x Calculation: To calculate f ( n ) ( x ) for f ( x ) = sin x First, taking n = 4 m + r , let’s take m = 0 Then n = r i.e. n = 4 ( 0 ) + r = r Thus, f ( n ) ( x ) = f ( 4 m + r ) ( x ) = f ( r ) ( x ) Now for m = 0 and r = 0 f ( n ) ( x ) = f ( 4 m + r ) ( x ) = f ( 0 + 0 ) ( x ) = f ( 0 ) ( x ) = f ( x ) = sin x For m = 0 and r = 1 f ( n ) ( x ) = f ( 4 m + r ) ( x ) = f ( 0 + 1 ) ( x ) = f ( 1 ) ( x ) = d d x ( f ( x ) ) = d d x ( sin x ) = cos x For m = 0 and r = 2 f ( n ) ( x ) = f ( 4 m + r ) ( x ) = f ( 0 + 2 )

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 3.6, Problem 45E

To determine

For f(x)=sinx , compute fn(x) by taking n=4m+r , where m is a whole number and r=0,1,2 or 3. Compute fn(x) from r and explain how to do latter step.

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Chapter 3.6, Problem 44E

Chapter 3.6, Problem 46E

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f'(x)

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Chapter 3 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

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Prob. 46E Ch. 3.9 - Prob. 47E Ch. 3.9 - Prob. 48E Ch. 3.9 - Prob. 49E Ch. 3.9 - Prob. 50E Ch. 3.9 - Prob. 51E Ch. 3.9 - Prob. 52E Ch. 3.9 - Prob. 53E Ch. 3.9 - Prob. 54E Ch. 3.9 - Prob. 55E Ch. 3.9 - Prob. 56E Ch. 3.9 - Prob. 57E Ch. 3.9 - Prob. 58E Ch. 3.9 - Prob. 59E Ch. 3.9 - Prob. 60E Ch. 3.9 - Prob. 61E Ch. 3.9 - Prob. 62E Ch. 3.9 - Prob. 63E Ch. 3.9 - Prob. 64E Ch. 3.9 - Prob. 65E Ch. 3.9 - Prob. 66E Ch. 3.9 - Prob. 67E Ch. 3.9 - Prob. 68E Ch. 3.9 - Prob. 69E Ch. 3.9 - Prob. 70E Ch. 3.9 - Prob. 71E Ch. 3.9 - Prob. 72E Ch. 3.9 - Prob. 73E Ch. 3.9 - Prob. 74E Ch. 3.9 - Prob. 75E Ch. 3.9 - Prob. 76E Ch. 3.9 - Prob. 77E Ch. 3.9 - Prob. 78E Ch. 3.9 - Prob. 79E Ch. 3.9 - Prob. 80E Ch. 3.9 - Prob. 81E Ch. 3.9 - Prob. 82E Ch. 3.9 - Prob. 83E Ch. 3.9 - Prob. 84E Ch. 3.9 - Prob. 85E Ch. 3.9 - Prob. 86E Ch. 3.9 - Prob. 87E Ch. 3.9 - Prob. 88E Ch. 3.10 - Prob. 1PQ Ch. 3.10 - Prob. 2PQ Ch. 3.10 - Prob. 3PQ Ch. 3.10 - Prob. 4PQ Ch. 3.10 - Prob. 5PQ Ch. 3.10 - Prob. 6PQ Ch. 3.10 - Prob. 1E Ch. 3.10 - Prob. 2E Ch. 3.10 - Prob. 3E Ch. 3.10 - Prob. 4E Ch. 3.10 - Prob. 5E Ch. 3.10 - Prob. 6E Ch. 3.10 - Prob. 7E Ch. 3.10 - Prob. 8E Ch. 3.10 - Prob. 9E Ch. 3.10 - Prob. 10E Ch. 3.10 - Prob. 11E Ch. 3.10 - Prob. 12E Ch. 3.10 - Prob. 13E Ch. 3.10 - Prob. 14E Ch. 3.10 - Prob. 15E Ch. 3.10 - Prob. 16E Ch. 3.10 - Prob. 17E Ch. 3.10 - Prob. 18E Ch. 3.10 - Prob. 19E Ch. 3.10 - Prob. 20E Ch. 3.10 - Prob. 21E Ch. 3.10 - Prob. 22E Ch. 3.10 - Prob. 23E Ch. 3.10 - Prob. 24E Ch. 3.10 - Prob. 25E Ch. 3.10 - Prob. 26E Ch. 3.10 - Prob. 27E Ch. 3.10 - Prob. 28E Ch. 3.10 - Prob. 29E Ch. 3.10 - Prob. 30E Ch. 3.10 - Prob. 31E Ch. 3.10 - Prob. 32E Ch. 3.10 - Prob. 33E Ch. 3.10 - Prob. 34E Ch. 3.10 - Prob. 35E Ch. 3.10 - Prob. 36E Ch. 3.10 - Prob. 37E Ch. 3.10 - Prob. 38E Ch. 3.10 - Prob. 39E Ch. 3.10 - Prob. 40E Ch. 3.10 - Prob. 41E Ch. 3.10 - Prob. 42E Ch. 3.10 - Prob. 43E Ch. 3.10 - Prob. 44E Ch. 3.10 - Prob. 45E Ch. 3 - Prob. 1CRE Ch. 3 - Prob. 2CRE Ch. 3 - Prob. 3CRE Ch. 3 - Prob. 4CRE Ch. 3 - Prob. 5CRE Ch. 3 - Prob. 6CRE Ch. 3 - Prob. 7CRE Ch. 3 - Prob. 8CRE Ch. 3 - Prob. 9CRE Ch. 3 - Prob. 10CRE Ch. 3 - Prob. 11CRE Ch. 3 - Prob. 12CRE Ch. 3 - Prob. 13CRE Ch. 3 - Prob. 14CRE Ch. 3 - Prob. 15CRE Ch. 3 - Prob. 16CRE Ch. 3 - Prob. 17CRE Ch. 3 - Prob. 18CRE Ch. 3 - Prob. 19CRE Ch. 3 - Prob. 20CRE Ch. 3 - Prob. 21CRE Ch. 3 - Prob. 22CRE Ch. 3 - Prob. 23CRE Ch. 3 - Prob. 24CRE Ch. 3 - Prob. 25CRE Ch. 3 - Prob. 26CRE Ch. 3 - Prob. 27CRE Ch. 3 - Prob. 28CRE Ch. 3 - Prob. 29CRE Ch. 3 - Prob. 30CRE Ch. 3 - Prob. 31CRE Ch. 3 - Prob. 32CRE Ch. 3 - Prob. 33CRE Ch. 3 - Prob. 34CRE Ch. 3 - Prob. 35CRE Ch. 3 - Prob. 36CRE Ch. 3 - Prob. 37CRE Ch. 3 - Prob. 38CRE Ch. 3 - Prob. 39CRE Ch. 3 - Prob. 40CRE Ch. 3 - Prob. 41CRE Ch. 3 - Prob. 42CRE Ch. 3 - Prob. 43CRE Ch. 3 - Prob. 44CRE Ch. 3 - Prob. 45CRE Ch. 3 - Prob. 46CRE Ch. 3 - Prob. 47CRE Ch. 3 - Prob. 48CRE Ch. 3 - Prob. 49CRE Ch. 3 - Prob. 50CRE Ch. 3 - Prob. 51CRE Ch. 3 - Prob. 52CRE Ch. 3 - Prob. 53CRE Ch. 3 - Prob. 54CRE Ch. 3 - Prob. 55CRE Ch. 3 - Prob. 56CRE Ch. 3 - Prob. 57CRE Ch. 3 - Prob. 58CRE Ch. 3 - Prob. 59CRE Ch. 3 - Prob. 60CRE Ch. 3 - Prob. 61CRE Ch. 3 - Prob. 62CRE Ch. 3 - Prob. 63CRE Ch. 3 - Prob. 64CRE Ch. 3 - Prob. 65CRE Ch. 3 - Prob. 66CRE Ch. 3 - Prob. 67CRE Ch. 3 - Prob. 68CRE Ch. 3 - Prob. 69CRE Ch. 3 - Prob. 70CRE Ch. 3 - Prob. 71CRE Ch. 3 - Prob. 72CRE Ch. 3 - Prob. 73CRE Ch. 3 - Prob. 74CRE Ch. 3 - Prob. 75CRE Ch. 3 - Prob. 76CRE Ch. 3 - Prob. 77CRE Ch. 3 - Prob. 78CRE Ch. 3 - Prob. 79CRE Ch. 3 - Prob. 80CRE Ch. 3 - Prob. 81CRE Ch. 3 - Prob. 82CRE Ch. 3 - Prob. 83CRE Ch. 3 - Prob. 84CRE Ch. 3 - Prob. 85CRE Ch. 3 - Prob. 86CRE Ch. 3 - Prob. 87CRE Ch. 3 - Prob. 88CRE Ch. 3 - Prob. 89CRE Ch. 3 - Prob. 90CRE Ch. 3 - Prob. 91CRE Ch. 3 - Prob. 92CRE Ch. 3 - Prob. 93CRE Ch. 3 - Prob. 94CRE Ch. 3 - Prob. 95CRE Ch. 3 - Prob. 96CRE Ch. 3 - Prob. 97CRE Ch. 3 - Prob. 98CRE Ch. 3 - Prob. 99CRE Ch. 3 - Prob. 100CRE Ch. 3 - Prob. 101CRE Ch. 3 - Prob. 102CRE Ch. 3 - Prob. 103CRE Ch. 3 - Prob. 104CRE Ch. 3 - Prob. 105CRE Ch. 3 - Prob. 106CRE Ch. 3 - 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For f ( x ) = sin x , compute f n ( x ) by taking n = 4 m + r , where m is a whole number and r = 0 , 1 , 2 or 3. Compute f n ( x ) from r and explain how to do latter step.

Solution Summary: The author explains how to compute fn(x) from r.

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For f(x)=sinx , compute fn(x) by taking n=4m+r , where m is a whole number and r=0,1,2 or 3. Compute fn(x) from r and explain how to do latter step.

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Chapter 3 Solutions