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...
Related questions
Question
![**Implicit Differentiation: Finding the Slope**
Find the equation of the line tangent to the hyperbola \( x^2 + 2xy - y^2 + x = 5 \) at the point \( (3, 7) \).
---
**Step 1**
*Graph Explanation:*
The graph shows a hyperbola on a coordinate plane. The axes range from -10 to 10. The curves of the hyperbola intersect the axes, and there is a tangent line at the point (3, 7).
*Instructions:*
Use implicit differentiation to find the slope of the tangent line to the hyperbola
\[ x^2 + 2xy - y^2 + x = 5 \]
at the point \( (3, 7) \).
\[
\frac{d}{dx}[x^2 + 2xy - y^2 + x] = \frac{d}{dx}[5]
\]
Taking the derivative of both sides with respect to \( x \) gives:
\[
2x + 2 \left( y + x \frac{dy}{dx} \right) - 2y \frac{dy}{dx} + 1 = 0
\]
---
*Options:*
- Submit
- Skip, (you cannot come back)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27af745b-6d4f-4129-9ebf-5574c17547e0%2F152c269d-3422-48a1-8791-525105a4fff1%2F67oh3jp_processed.png&w=3840&q=75)
Transcribed Image Text:**Implicit Differentiation: Finding the Slope**
Find the equation of the line tangent to the hyperbola \( x^2 + 2xy - y^2 + x = 5 \) at the point \( (3, 7) \).
---
**Step 1**
*Graph Explanation:*
The graph shows a hyperbola on a coordinate plane. The axes range from -10 to 10. The curves of the hyperbola intersect the axes, and there is a tangent line at the point (3, 7).
*Instructions:*
Use implicit differentiation to find the slope of the tangent line to the hyperbola
\[ x^2 + 2xy - y^2 + x = 5 \]
at the point \( (3, 7) \).
\[
\frac{d}{dx}[x^2 + 2xy - y^2 + x] = \frac{d}{dx}[5]
\]
Taking the derivative of both sides with respect to \( x \) gives:
\[
2x + 2 \left( y + x \frac{dy}{dx} \right) - 2y \frac{dy}{dx} + 1 = 0
\]
---
*Options:*
- Submit
- Skip, (you cannot come back)
Expert Solution
Step 1
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning