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Second derivative Assume a curve is given by the parametric equations x = f(t) and y = g(t), where f and g are twice differ- entiable. Use the Chain Rule to show that f'(t)g"(t) – g'(t)f"(t) y"(x) = (f'(1))³

Second derivative Assume a curve is given by the parametric equations x = f(t) and y = g(t), where f and g are twice differ- entiable. Use the Chain Rule to show that f'(t)g"(t) – g'(t)f"(t) y"(x) = (f'(1))³

Calculus: Early Transcendentals
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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Second derivative Assume a curve is given by the parametric equations x = f(t) and y = g(t), where f and g are twice differ- entiable. Use the Chain Rule to show that f'(t)g"(t) – g'(t)f"(t) y"(x) = (f'(1))³
Transcribed Image Text:Second derivative Assume a curve is given by the parametric equations x = f(t) and y = g(t), where f and g are twice differ- entiable. Use the Chain Rule to show that f'(t)g"(t) – g'(t)f"(t) y"(x) = (f'(1))³
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