Explanation Given information: The function is f ( x ) = ( x 3 + 2 x + 1 ) ( 2 + 1 x 2 ) . Formula used : (1). The product rule of differentiation is, f ′ ( x ) = d d x [ f ( x ) ⋅ g ( x ) ] = f ( x ) ⋅ d d x g ( x ) + g ( x ) ⋅ d d x f ( x ) (2). The power rule of derivate is d d x ( x n ) = n x n − 1 . Calculation: Use product rule of differentiation to find the derivative of the function. f ′ ( x ) = d d x [ ( x 3 + 2 x + 1 ) ( 2 + 1 x 2 ) ] = ( x 3 + 2 x + 1 ) d d x ( 2 + 1 x 2 ) + ( 2 + 1 x 2 ) d d x ( x 3 + 2 x + 1 ) (1) Use the power rule to find the derivate of term ( 2 + 1 x 2 ) . d d x ( 2 + 1 x 2 ) = d d x ( 2 ) + d d x ( 1 x 2 ) = 0 + d d x ( x − 2 ) = − 2 x − 3 = − 2 x 3 Use the power rule to find the derivate of term ( x 3 + 2 x + 1 )

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ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

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Chapter 3.2, Problem 14E

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To find: The derivative of given function.

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Chapter 3.2, Problem 13E

Chapter 3.2, Problem 15E

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Determine whether the function is not differentiable using differentiability and continuity, and show the complete solution, thank you so much

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The derivative of given function.

Solution Summary: The author explains how to find the derivative of a given function by using the product rule of differentiation.

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Chapter 3 Solutions