To find: The equation of the tangent line to the given equation at the point.
Answer to Problem 23E
The equation of the tangent line to the equation
Explanation of Solution
Given:
The equation 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,
Therefore, the derivative of y 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