Instantaneous Rate of Change Problem

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To find the instantaneous rate of change for the function y² + (xy + 1)³ = 0 at the point (2, -1), implicit differentiation is recommended. The user struggles with isolating y due to the mixed powers of y in the equation. The suggested approach involves differentiating both sides of the equation with respect to x while applying the chain rule. This method will help derive dy/dx, which represents the instantaneous rate of change at the specified point. Utilizing implicit differentiation is essential for solving this type of problem effectively.
claytonh4
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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!
 
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claytonh4 said:

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.
 

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