Explanation Given: Function f ( x ) = x 2 ( x 3 + 5 ) . Formula Used: Product rule of derivative is as follows: ( f . g ) ′ = f ′ . g + f . g ′ Calculation: Function is given as f ( x ) = x 2 ( x 3 + 5 ) . We need to calculate the derivative of above function. Method 1: Calculating derivative using product rule f ′ ( x ) = [ d d x ( x 2 ) × ( x 3 + 5 ) ] + [ ( x 2 ) × d d x ( x 3 + 5 ) ] f ′ ( x ) = [ ( 2 x ) ( x 3 + 5 ) ] + [ ( x 2 ) ( 3 x 2 ) ] f ′ ( x ) = 2 x 4 + 10 x + 3 x 4 f ′ ( x ) = 5 x 4 + 10 x Method 2: Multiplying before calculating the derivative

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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Question

Chapter 3.4, Problem 1P

To determine

To find f′(x) in two ways − by using the product rule and by multiplying out before taking the derivative.

f(x)=x2(x3+5)

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Chapter 3.3, Problem 53P

Chapter 3.4, Problem 2P

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Chapter 3 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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To find f ′ ( x ) in two ways − by using the product rule and by multiplying out before taking the derivative. f ( x ) = x 2 ( x 3 + 5 )

Solution Summary: The author explains how to calculate the derivative of fprime(x) using the product rule and by multiplying before calculating it.

Videos

To find f′(x) in two ways − by using the product rule and by multiplying out before taking the derivative.

f(x)=x2(x3+5)

Want to see the full answer?

Chapter 3 Solutions

To find f ′ ( x ) in two ways − by using the product rule and by multiplying out before taking the derivative. f ( x ) = x 2 ( x 3 + 5 )

Solution Summary: The author explains how to calculate the derivative of fprime(x) using the product rule and by multiplying before calculating it.

Videos

To find f′(x) in two ways − by using the product rule and by multiplying out before taking the derivative. f(x)=x2(x3+5)

Want to see the full answer?

Chapter 3 Solutions

To find f′(x) in two ways − by using the product rule and by multiplying out before taking the derivative.

f(x)=x2(x3+5)