# How do you use implicit differentiation to find an equation of the tangent line to the curve #x^2 + 2xy − y^2 + x = 39# at the given point (5, 9)?

##### 2 Answers

#### Explanation:

Differentiate the equation with respect to

The equation of the tangent line is:

where

then:

or:

is the equation of the tangent

#### Explanation:

Given:

when x=5, and y=9

verified

We have

Differentiating both sides wrt x

Substituting x=5 and y=9

Slope of the tangent is

Passing through the point

Equation of the tangent is