Directions: Use the equation given below to answer the following questions. x² - xy - y² = 5 Part 1: Derivative dy Calculate the derivative by implicit differentiation: da dy dr Part 2: Tangent Line Find an equation of the tangent line to the curve at the point (3, 1). Tangent Line: y =

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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**Directions:** Use the equation given below to answer the following questions.

\[ x^2 - xy - y^2 = 5 \]

---

**Part 1: Derivative**

Calculate the derivative \(\frac{dy}{dx}\) by implicit differentiation:

\[
\frac{dy}{dx} = \_\_\_\_
\]

---

**Part 2: Tangent Line**

Find an equation of the tangent line to the curve at the point \((3, 1)\).

Tangent Line: \( y = \_\_\_\_ \)
Transcribed Image Text:**Directions:** Use the equation given below to answer the following questions. \[ x^2 - xy - y^2 = 5 \] --- **Part 1: Derivative** Calculate the derivative \(\frac{dy}{dx}\) by implicit differentiation: \[ \frac{dy}{dx} = \_\_\_\_ \] --- **Part 2: Tangent Line** Find an equation of the tangent line to the curve at the point \((3, 1)\). Tangent Line: \( y = \_\_\_\_ \)
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