Suppose that and y are both differentiable functions of t and are related by the equation y³ + x³ = 12. 1. Use implicit differentiation with respect to t to determine dy dt 2. Calculate dy dt dx dt when x = 1, y = -2, and da dt dy dt in terms of x, y, and = 2. Type your answer here dx dt Give your answer as an integer or a fraction.
Suppose that and y are both differentiable functions of t and are related by the equation y³ + x³ = 12. 1. Use implicit differentiation with respect to t to determine dy dt 2. Calculate dy dt dx dt when x = 1, y = -2, and da dt dy dt in terms of x, y, and = 2. Type your answer here dx dt Give your answer as an integer or a fraction.
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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![Suppose that \( x \) and \( y \) are both differentiable functions of \( t \) and are related by the equation \( y^3 + x^3 = 12 \).
1. Use implicit differentiation with respect to \( t \) to determine \( \frac{dy}{dt} \) in terms of \( x, y, \) and \( \frac{dx}{dt} \).
\[
\frac{dy}{dt} = \ \_\_\_\_ \ . \frac{dx}{dt}
\]
2. Calculate \( \frac{dy}{dt} \) when \( x = 1, \ y = -2, \) and \( \frac{dx}{dt} = 2 \). Type your answer here \_\_\_\_. Give your answer as an integer or a fraction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d3fcd68-35a4-43ef-98ae-7c8729ad0bef%2Fe98aa85c-8faf-40a1-9665-7158864f7680%2Foi1jig_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that \( x \) and \( y \) are both differentiable functions of \( t \) and are related by the equation \( y^3 + x^3 = 12 \).
1. Use implicit differentiation with respect to \( t \) to determine \( \frac{dy}{dt} \) in terms of \( x, y, \) and \( \frac{dx}{dt} \).
\[
\frac{dy}{dt} = \ \_\_\_\_ \ . \frac{dx}{dt}
\]
2. Calculate \( \frac{dy}{dt} \) when \( x = 1, \ y = -2, \) and \( \frac{dx}{dt} = 2 \). Type your answer here \_\_\_\_. Give your answer as an integer or a fraction.
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