Explanation Given: The function, f ( x ) = 1 − x e x x + e x . Concept Used: The quotient rule of derivatives: d d x [ f ( x ) g ( x ) ] = g ( x ) ⋅ d d x f ( x ) − f ( x ) ⋅ d d x g ( x ) ( g ( x ) ) 2 The product rule of derivatives: d d x [ f ( x ) ⋅ g ( x ) ] = f ( x ) ⋅ d d x g ( x ) + g ( x ) ⋅ d d x f ( x ) Power rule of derivatives: d d x ( x n ) = n x n − 1 d d x ( e x ) = e x Calculation: In order to find the derivative of the given function, use the quotient rule of derivatives. Observe that the given function is a quotient of two functions ( 1 − x e x ) and ( x + e x ) . So, using the quotient rule, product rule, and power rule of derivatives, it gives f ' ( x ) = d d x ( 1 − x e x x + e x ) = ( x + e x ) ⋅ d d x ( 1 − x e x ) − ( 1 − x e x ) ⋅ d d x ( x + e x ) ( x + e x ) 2 = ( x + e x ) ⋅ ( 0 − ( x ⋅ d d x ( e x ) + e x ⋅ d d x ( x ) ) ) − ( 1 − x e x ) ⋅ ( 1 + e x ) ( x +

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ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Question

Chapter 3.4, Problem 32E

To determine

The derivative of the function, f(x)=1−xexx+ex .

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Chapter 3.4, Problem 31E

Chapter 3.4, Problem 33E

Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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The derivative of the function, f ( x ) = 1 − x e x x + e x .

Solution Summary: The author explains the quotient rule of derivatives to find the derivative of the given function.

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The derivative of the function, f(x)=1−xexx+ex .

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