To find: The equation of the tangent line to the given equation at the point.
Answer to Problem 24E
The equation of the tangent line to the equation
Explanation of Solution
Given:
The curve is
The point is
Derivative rules:
(1) Chain rule: If
(2) Product rule: If
Formula used:
The equation of the tangent line at
where, m is the slope of the tangent line at
Calculation:
Consider the equation
Differentiate the above equation implicitly with respect to x,
Apply the product rule (2),
Apply the chain rule (1) and simplify the terms,
Combine the terms
Therefore, the derivative of the equation is
The slope of the tangent line at
Thus, the slope of the tangent line at
Substitute
Therefore, the equation of the tangent line to the equation
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning