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12. Find y (a) tan-1! 3m(22 +y7) %3D (b) y = ¤V= (ejal a %3D

12. Find y (a) tan-1! 3m(22 +y7) %3D (b) y = ¤V= (ejal a %3D

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 12:** (a) Find \( y' \) if \( \tan^{-1} \frac{y}{x} = \frac{1}{2} \ln(x^2 + y^2) \). (b) \( y = x\sqrt{x} \). --- **Explanation for Educational Context:** This problem requires you to find the derivative \( y' \) for two different equations. - **Part (a)** involves implicit differentiation of the equation involving inverse tangent \(\tan^{-1}\) and logarithmic functions. - **Part (b)** involves finding the derivative of a function \( y = x\sqrt{x} \), which simplifies to \( y = x^{3/2} \). You will need to apply power rule differentiation to solve this part.
Transcribed Image Text:**Problem 12:** (a) Find \( y' \) if \( \tan^{-1} \frac{y}{x} = \frac{1}{2} \ln(x^2 + y^2) \). (b) \( y = x\sqrt{x} \). --- **Explanation for Educational Context:** This problem requires you to find the derivative \( y' \) for two different equations. - **Part (a)** involves implicit differentiation of the equation involving inverse tangent \(\tan^{-1}\) and logarithmic functions. - **Part (b)** involves finding the derivative of a function \( y = x\sqrt{x} \), which simplifies to \( y = x^{3/2} \). You will need to apply power rule differentiation to solve this part.
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