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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.5, Problem 23E

To determine

**To find:** The equation of the tangent line to the given equation at the point.

Expert Solution

The equation of the tangent line to the equation

**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