Really? TheEmptySet actually used a shortcut from multivariable Calculus. He didn't do it by implicit differentiation and then solving for dy/dx. If you would like to, show us how you did the problem so others may use this thread in the future as a reference.
Oh ok. You didn't do implicit differentiation. You used partial differentiation. That is fine of course I just assumed by the thread title that you were in a Calc I or II class, not Calc III.
Really? TheEmptySet actually used a shortcut from multivariable Calculus. He didn't do it by implicit differentiation and then solving for dy/dx. If you would like to, show us how you did the problem so others may use this thread in the future as a reference.
eeppp I need to pay more attention. I thought that is what we wanted. I will add this for completeness
Suppose and that
then we get
then by implict differentation and the chain rule we get