Gottfried Leibniz, one of the inventors of calculus, initially thought that the derivative of f(x)g(x) was f'(x)g'(x), based on the example f(x) = x² + bx and g(x) = cx + d. Besides neglecting to work out the details, which would have shown his error, he made an erroneous conclusion based on one example, rather than a mathematical proof. Source: PRIMUS. (a) Calculate f'(x)g'(x). (b) Calculate [f(x)g(x)]'; and verify that your answer is differ- ent than your answer to part (a).
Gottfried Leibniz, one of the inventors of calculus, initially thought that the derivative of f(x)g(x) was f'(x)g'(x), based on the example f(x) = x² + bx and g(x) = cx + d. Besides neglecting to work out the details, which would have shown his error, he made an erroneous conclusion based on one example, rather than a mathematical proof. Source: PRIMUS. (a) Calculate f'(x)g'(x). (b) Calculate [f(x)g(x)]'; and verify that your answer is differ- ent than your answer to part (a).
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Gottfried Leibniz, one of the inventors of calculus, initially
thought that the derivative of f(x)g(x) was f'(x)g'(x), based
on the example f(x) = x² + bx and g(x) = cx + d. Besides
neglecting to work out the details, which would have shown his
error, he made an erroneous conclusion based on one example,
rather than a mathematical proof. Source: PRIMUS.
(a) Calculate f'(x)g'(x).
(b) Calculate [f(x)g(x)]'; and verify that your answer is differ-
ent than your answer to part (a).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d1a24c4-85a6-4ae6-82e8-3581574697ec%2F6f65239d-de05-40e9-8cd4-a41d89be4585%2Fulnbxt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Gottfried Leibniz, one of the inventors of calculus, initially
thought that the derivative of f(x)g(x) was f'(x)g'(x), based
on the example f(x) = x² + bx and g(x) = cx + d. Besides
neglecting to work out the details, which would have shown his
error, he made an erroneous conclusion based on one example,
rather than a mathematical proof. Source: PRIMUS.
(a) Calculate f'(x)g'(x).
(b) Calculate [f(x)g(x)]'; and verify that your answer is differ-
ent than your answer to part (a).
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