Question

How do you find `dy/dx` by implicit differentiation given `x^-2+y^-2=1`?

Answer 1

`dy/dx=-y^3/x^3`

Explanation:

`x^-2+y^-2=1`

Using the Power Rule and Implicit Differentiation

`-2x^-3 -2y^-3 dy/dx = 0`

`-2y^-3 dy/dx = 2x^-3`

`dy/dx = (2x^-3)/(-2y^-3) = -y^3/x^3`