Explanation Given: Function f ( x ) = ( 2 x + 1 ) ( 3 x − 2 ) . Formula Used: Product rule of derivative is as follows: ( f . g ) ′ = f ′ . g + f . g ′ Calculation: Function is given as f ( x ) = ( 2 x + 1 ) ( 3 x − 2 ) . We need to calculate the derivative of above function. Method 1: Calculating derivative using product rule. f ′ ( x ) = [ d d x ( 2 x + 1 ) × ( 3 x − 2 ) ] + [ ( 2 x + 1 ) × d d x ( 3 x − 2 ) ] f ′ ( x ) = [ ( 2 ) ( 3 x − 2 ) ] + [ ( 2 x + 1 ) ( 3 ) ] f ′ ( x ) = 6 x − 4 + 6 x + 3 f ′ ( x ) = 12 x − 1 Method 2: Multiplying before calculating the derivative

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 3.4, Problem 2P

To determine

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

f(x)=(2x+1)(3x−2)

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Chapter 3.4, Problem 1P

Chapter 3.4, Problem 3P

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APPLIED CALCULUS-PRINT COMPANION (LL)

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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 ) = ( 2 x + 1 ) ( 3 x − 2 )

Solution Summary: The author explains how to calculate the derivative of the function by using the product rule and by multiplying out before calculating it.

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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)=(2x+1)(3x−2)

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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 ) = ( 2 x + 1 ) ( 3 x − 2 )

Solution Summary: The author explains how to calculate the derivative of the function by using the product rule and by multiplying out before calculating it.

Concept explainers

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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)=(2x+1)(3x−2)

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)=(2x+1)(3x−2)