# Find all points on the curve #x^2y^2+xy=2# where the slope of the tangent line is #-1#?

##### 1 Answer

Use Implicit Differentiation (and hope it all falls out the bottom)

Differentiate both sides of the equation:

using the product rule (a couple of times) and the chain rule:

giving

or

We are asked for the points where the slope (

so

or

provided

we have

The original equation becomes

since

with (as already determined

the required points are