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10. Find at x = 1, if e*y+1 = 3 dx A. In 3 B. In 3 – 1 С. 1 — In 3 D. In 3 1 E. e³ In(3) F. None of the above

10. Find at x = 1, if e*y+1 = 3 dx A. In 3 B. In 3 – 1 С. 1 — In 3 D. In 3 1 E. e³ In(3) F. None of the above

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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**Problem 10: Differential Calculus** Find \(\frac{dy}{dx}\) at \(x = 1\), if \(e^{xy+1} = 3\). **Options:** A. \(\ln 3\) B. \(\ln 3 - 1\) C. \(1 - \ln 3\) D. \(\frac{1}{\ln 3}\) E. \(e^3 \ln(3)\) F. None of the above This problem involves finding the derivative \(\frac{dy}{dx}\) using implicit differentiation from the given exponential equation. The solution involves applying differentiation rules and evaluating the expression at the specified value of \(x\).
Transcribed Image Text:**Problem 10: Differential Calculus** Find \(\frac{dy}{dx}\) at \(x = 1\), if \(e^{xy+1} = 3\). **Options:** A. \(\ln 3\) B. \(\ln 3 - 1\) C. \(1 - \ln 3\) D. \(\frac{1}{\ln 3}\) E. \(e^3 \ln(3)\) F. None of the above This problem involves finding the derivative \(\frac{dy}{dx}\) using implicit differentiation from the given exponential equation. The solution involves applying differentiation rules and evaluating the expression at the specified value of \(x\).
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