Explanation Given Information: The function is y = x ( x − 5 ) ( x − 4 ) . Formula used: Quotient 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 ) [ g ( x ) ] 2 Where, g ( x ) ≠ 0 . 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 . 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 = x ( x − 5 ) ( x − 4 ) . Apply quotient rule of derivative, d y d x = d d x x ⋅ ( x − 5 ) ( x − 4 ) − x d d x ( x − 5 ) ( x − 4 ) [ ( x − 5 ) ( x − 4 ) ] 2 Apply product rule to the product ( x − 5 ) ( x − 4 ) , d d x ( x − 5 ) ( x − 4 ) = d d x ( x − 5 ) ⋅ ( x − 4 ) + ( x − 5 ) ⋅ d d x ( x − 4 ) Apply difference rule, power rule and constant derivative rule, d d x ( x − 5 ) ( x − 4 ) = [ 1 x 1 − 1 −</

7th Edition

ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 4.3, Problem 54E

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To calculate: The derivative of function $y=x(x−5)(x−4)$ .

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Chapter 4.3, Problem 53E

Chapter 4.3, Problem 55E

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The derivative of function y = x ( x − 5 ) ( x − 4 ) .

Solution Summary: The author calculates the derivative of the function y=x(x-5) left (x-4) right.

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To calculate: The derivative of function $y=x(x−5)(x−4)$ .

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