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

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ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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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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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 ) = ( 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

Videos

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)