Instantaneous Rate of Change Problem

[claytonh4]

Homework Statement

Find the instantaneous rate of change for the function y²+(xy+1)³=0 at (2,-1)

Homework Equations

N/A

The Attempt at a Solution

I tried getting it into a "y=" format but I don't really understand how to deal with the y when it's squared in one part and cubed in the other. This is as far as I could figure:
y=(-(xy+1)³)^1/2

Thanks for any help!

 

[SammyS]

Homework Statement

Find the instantaneous rate of change for the function y²+(xy+1)³=0 at (2,-1)

Homework Equations

N/A

The Attempt at a Solution

I tried getting it into a "y=" format but I don't really understand how to deal with the y when it's squared in one part and cubed in the other. This is as far as I could figure:
y=(-(xy+1)³)^1/2

Thanks for any help!

Use implicit differentiation.