# How do you use implicit differentiation to find the slope of the curve given #xy^2+x^2y=2# at (1,-2)?

##### 2 Answers

Treat

#### Explanation:

Assuming the equation defines

This can be rearranged to

Plugging in the point

If it helps, conceptually-speaking, you could write

Since the original equation is quadratic in

See below

#### Explanation:

This particular equation will use the product and chain rule. When we differentiate implicitly, we use the idea of the chain rule when we differentiate

The

So from example:

Apply product and chain rule:

Plugging in our coordinates:

GRAPH: