Explanation Given: The function is f ( x ) = ( 3 x 2 + 1 ) ( 2 x − 1 ) 5 x + 4 . Formula used: (1) The quotient rule is: d d x [ u ( x ) v ( x ) ] = v ( x ) ⋅ u ' ( x ) − u ( x ) ⋅ v ' ( x ) ( v ( x ) ) 2 . (2). The product rule is: d d x [ u ( x ) ⋅ v ( x ) ] = u ( x ) ⋅ v ' ( x ) + v ( x ) ⋅ u ' ( x ) . (3). The sum rule : d d x ( u ( x ) + v ( x ) ) = d d x ( u ( x ) ) + d d x ( v ( x ) ) . (4). The difference rule : d d x ( u ( x ) + v ( x ) ) = d d x ( u ( x ) ) + d d x ( v ( x ) ) . (5). The power rule: d d x ( x n ) = n x n − 1 . (6). The constant rule: d d x ( k ) = 0 . Calculation: Let u ( x ) = ( 3 x 2 + 1 ) ( 2 x − 1 ) and v ( x ) = 5 x + 4 . Apply the quotient rule for the given function f ( x ) = ( 3 x 2 + 1 ) ( 2 x − 1 ) 5 x + 4 as follows. f ' ( x ) = d d x [ ( 3 x 2 + 1 ) ( 2 x − 1 ) 5 x + 4 ] = ( 5 x + 4 ) d d x ( ( 3 x 2 + 1 ) ( 2 x − 1 ) ) − ( ( 3 x 2 + 1 ) ( 2 x − 1 ) ) ⋅ d d x ( 5 x + 4 ) ( 5 x + 4 ) 2 Apply the product rule for the term d d x ( ( 3 x 2 + 1 ) ( 2 x − 1 ) ) as follows. f ' ( x ) = ( 5 x + 4 ) ( ( 3 x 2 + 1 ) d d x ( 2 x − 1 ) + ( 2 x − 1 ) d d x ( ( 3 x 2 + 1 ) ) ) ( 5 x + 4 ) 2 − ( ( 3 x 2 + 1 ) ( 2 x − 1 ) ) ⋅ d d x ( 5 x + 4 ) ( 5 x + 4 ) 2 Apply the sum and difference rule as follows

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Chapter 4.2, Problem 27E

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To find: The derivative of the given function.

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Ch. 4.1 - YOUR TURN 1 find f′(t). Ch. 4.1 - YOUR TURN 2 find dy/dx. Ch. 4.1 - Prob. 3YT Ch. 4.1 - Prob. 4YT Ch. 4.1 - Prob. 5YT Ch. 4.1 - Prob. 1WE Ch. 4.1 - Prob. 2WE Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...

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