Explanation Given: The given statement is: “If f and g are differentiable functions, then d d x [ f ( x ) g ( x ) ] = f ′ ( x ) g ′ ( x ) ” Concept Used: Product rule of differentiation is: d d x [ f ( x ) g ( x ) ] = g ( x ) f ′ ( x ) + f ( x ) g ′ ( x ) st

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 3, Problem 4TFQ

To determine

To state if the given statement is true or false

“If f and g are differentiable functions, then ddx[f(x)g(x)]=f′(x)g′(x) ”

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Chapter 3, Problem 3TFQ

Chapter 3, Problem 5TFQ

Chapter 3 Solutions

Biocalculus

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

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Inverse Functions; Author: Professor Dave Explains;https://www.youtube.com/watch?v=9fJsrnE1go0;License: Standard YouTube License, CC-BY

To state if the given statement is true or false “If f and g are differentiable functions, then d d x [ f ( x ) g ( x ) ] = f ′ ( x ) g ′ ( x ) ”

Solution Summary: The author explains that if f and g are differentiable functions, then the given statement is false.

Concept explainers

Videos

To state if the given statement is true or false

“If f and g are differentiable functions, then ddx[f(x)g(x)]=f′(x)g′(x) ”

Want to see the full answer?

Chapter 3 Solutions

To state if the given statement is true or false “If f and g are differentiable functions, then d d x [ f ( x ) g ( x ) ] = f ′ ( x ) g ′ ( x ) ”

Solution Summary: The author explains that if f and g are differentiable functions, then the given statement is false.

Concept explainers

Videos

To state if the given statement is true or false “If f and g are differentiable functions, then ddx[f(x)g(x)]=f′(x)g′(x) ”

Want to see the full answer?

Chapter 3 Solutions

To state if the given statement is true or false

“If f and g are differentiable functions, then ddx[f(x)g(x)]=f′(x)g′(x) ”