Explanation Given Information: The provided function is y = ( 2 x 2 − 4 x + 1 ) 2 . Formula used: Product rule of derivative of differentiable functions, f ( x ) and g ( x ) is, d d x [ f ( x ) g ( x ) ] = f ' ( x ) g ( x ) + f ( x ) g ' ( x ) Derivative of function y = x n using power rule is d y d x = n x n − 1 . Derivative of a constant is 0 . Constant multiple rule of derivative of function f ( x ) is d d x [ c f ( x ) ] = c d d x [ f ( x ) ] where, c is constant. Sum and difference rule of derivative is d d x [ f ( x ) ± g ( x ) ] = d d x [ f ( x ) ] ± d d x [ g ( x ) ] where, f ( x ) and g ( x ) are any two differentiable functions. Calculation: Consider the function, y = ( 2 x 2 − 4 x + 1 ) 2 Rewrite the function as the product of two binomials, y = ( 2 x 2 − 4 x + 1 ) 2 = ( 2 x 2 − 4 x + 1 ) ( 2 x 2 − 4 x + 1 ) Apply product rule of derivative, d y d x = d d x ( 2 x 2 − 4 x + 1 ) ⋅ ( 2 x 2 − 4 x + 1 ) + ( 2 x 2 − 4 x + 1 ) ⋅ d d x ( 2 x 2 − 4 x + 1 ) Apply sum and difference rule of derivative, d y d x = [ d d x

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 11.3, Problem 33E

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Chapter 11.3, Problem 32E

Chapter 11.3, Problem 34E

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The derivative of function y = ( 2 x 2 − 4 x + 1 ) 2 .

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