Use implicit differentiation to find dy/dx and d?y/dx?. x? + y? = 9 dy O A. x a?y y' dx2 x² + y? y3 dx dy O B. x d²y y' dx2 x+y? dx x dy x2-y y' dx2 Oc. dx ,2 dy x d?y x? + y? O D. dx y' dv2 2
Use implicit differentiation to find dy/dx and d?y/dx?. x? + y? = 9 dy O A. x a?y y' dx2 x² + y? y3 dx dy O B. x d²y y' dx2 x+y? dx x dy x2-y y' dx2 Oc. dx ,2 dy x d?y x? + y? O D. dx y' dv2 2
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 Statement:**
Use implicit differentiation to find \( \frac{dy}{dx} \) and \( \frac{d^2y}{dx^2} \).
Equation:
\[ x^2 + y^2 = 9 \]
**Answer Choices:**
A. \(\frac{dy}{dx} = -\frac{x}{y}, \quad \frac{d^2y}{dx^2} = -\frac{x^2+y^2}{y^3}\)
B. \(\frac{dy}{dx} = -\frac{x}{y}, \quad \frac{d^2y}{dx^2} = -\frac{x+y^2}{y^3}\)
C. \(\frac{dy}{dx} = -\frac{x}{y}, \quad \frac{d^2y}{dx^2} = -\frac{y-x^2}{y^2}\)
D. \(\frac{dy}{dx} = -\frac{x}{y}, \quad \frac{d^2y}{dx^2} = \frac{x^2+y^2}{y^2}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65e9754d-e7bf-4951-a913-18b478a6d2d4%2F373e1169-7754-4a30-a3a0-aa539ed922ab%2Fqg365e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Use implicit differentiation to find \( \frac{dy}{dx} \) and \( \frac{d^2y}{dx^2} \).
Equation:
\[ x^2 + y^2 = 9 \]
**Answer Choices:**
A. \(\frac{dy}{dx} = -\frac{x}{y}, \quad \frac{d^2y}{dx^2} = -\frac{x^2+y^2}{y^3}\)
B. \(\frac{dy}{dx} = -\frac{x}{y}, \quad \frac{d^2y}{dx^2} = -\frac{x+y^2}{y^3}\)
C. \(\frac{dy}{dx} = -\frac{x}{y}, \quad \frac{d^2y}{dx^2} = -\frac{y-x^2}{y^2}\)
D. \(\frac{dy}{dx} = -\frac{x}{y}, \quad \frac{d^2y}{dx^2} = \frac{x^2+y^2}{y^2}\)
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