Explanation Given: The functions sin ( x 2 + 1 ) and sin ( x 3 + 1 ) . Formula Used: Chain rule of derivative states that d d x f ( x ) = d f d u × d u d x d d x ( sin x ) = cos x d d x ( x n ) = n x n − 1 Calculation: We have sin ( x 2 + 1 ) and sin ( x 3 + 1 ) Consider the function sin ( x 2 + 1 ) . We need to calculate the derivative of above. d d x [ sin ( x 2 + 1 ) ] Let u = x 2 + 1 , f = sin u Applying chain rule of derivative, we have d d x sin ( x 2 + 1 ) = d d u ( sin u ) × d d x ( x 2 + 1 ) = ( cos u ) ( 2 x + 0 ) = ( cos u ) ( 2 x ) = 2 x cos u = 2 x cos ( x 2 + 1 ) Consider the function sin ( x 3 + 1 ) To determine (b) To find the antiderivative of x cos ( x 2 + 1 ) and x 2 cos ( x 3 + 1 ) using the result of part (a). To determine (c) To find the antiderivative of x sin ( x 2 + 1 ) and x 2 sin ( x 3 + 1 ) .

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 6.6, Problem 1P

To determine

(a)

To find the derivatives of sin(x2+1) and sin(x3+1).

To determine

(b)

To find the antiderivative of xcos(x2+1) and x2cos(x3+1) using the result of part (a).

To determine

(c)

To find the antiderivative of xsin(x2+1) and x2sin(x3+1).

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Chapter 6.5, Problem 24P

Chapter 6.6, Problem 2P

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Applied Calculus, 6e WileyPLUS + Loose-leaf

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(a) To find the derivatives of sin ( x 2 + 1 ) and sin ( x 3 + 1 ) .

Solution Summary: The author explains how to find the derivatives of mathrmsin(x2+1) and

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(a)

To find the derivatives of sin(x2+1) and sin(x3+1).

(b)

To find the antiderivative of xcos(x2+1) and x2cos(x3+1) using the result of part (a).

(c)

To find the antiderivative of xsin(x2+1) and x2sin(x3+1).

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Chapter 6 Solutions

(a) To find the derivatives of sin ( x 2 + 1 ) and sin ( x 3 + 1 ) .

Solution Summary: The author explains how to find the derivatives of mathrmsin(x2+1) and

Videos

(a) To find the derivatives of sin(x2+1) and sin(x3+1).

(b) To find the antiderivative of xcos(x2+1) and x2cos(x3+1) using the result of part (a).

(c) To find the antiderivative of xsin(x2+1) and x2sin(x3+1).

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Chapter 6 Solutions

(a)

To find the derivatives of sin(x2+1) and sin(x3+1).

(b)

To find the antiderivative of xcos(x2+1) and x2cos(x3+1) using the result of part (a).

(c)

To find the antiderivative of xsin(x2+1) and x2sin(x3+1).