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11. sin(x) + cos(y) = ey

11. sin(x) + cos(y) = ey

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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Number 11

### Implicit Differentiation Problems **6.** \(\ln(xy) = x\) **For problems 7 – 21, find \(y'\) by implicit differentiation.** **7.** \(y^2 - 12x^3 = 8y\) **8.** \(3y^7 + x^{10} = y^2 - 6x^3 + 2\) **9.** \(y^3 + 4x^1 = 8y^1\) **10.** \(10x^4 - y^6 = 7y^3 + 4x^3\) **11.** \(\sin(x) + \cos(y) = e^{4y}\) **12.** \(x + \ln(y) = \sec(y)\) **13.** \(y^2(4 - x^2) = y^7 + 9x\) **14.** \(6x^2 - x^3y^2 + 4x = 0\) **15.** \(8xy + 2x^1y^3 = x^3\) **16.** \(y^x - \cos(x)\sin(y) = 7x\) These exercises provide practice in finding the derivative \(y'\) using implicit differentiation techniques. Each problem presents a different level of complexity by involving various algebraic and transcendental expressions.
Transcribed Image Text:### Implicit Differentiation Problems **6.** \(\ln(xy) = x\) **For problems 7 – 21, find \(y'\) by implicit differentiation.** **7.** \(y^2 - 12x^3 = 8y\) **8.** \(3y^7 + x^{10} = y^2 - 6x^3 + 2\) **9.** \(y^3 + 4x^1 = 8y^1\) **10.** \(10x^4 - y^6 = 7y^3 + 4x^3\) **11.** \(\sin(x) + \cos(y) = e^{4y}\) **12.** \(x + \ln(y) = \sec(y)\) **13.** \(y^2(4 - x^2) = y^7 + 9x\) **14.** \(6x^2 - x^3y^2 + 4x = 0\) **15.** \(8xy + 2x^1y^3 = x^3\) **16.** \(y^x - \cos(x)\sin(y) = 7x\) These exercises provide practice in finding the derivative \(y'\) using implicit differentiation techniques. Each problem presents a different level of complexity by involving various algebraic and transcendental expressions.
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