Question

How do you implicitly differentiate `9=-y^2/x+x/y`?

Answer 1

`dy/dx = (2x-9y)/(3(3x +y^2))`

Explanation:

`9=-y^2/x+x/y`

`9xy=x^2-y^3`

`9xdy/dx + 9y = 2x - 3y^2dy/dx`
(Implicit differentiation, Product rule and Power rule)

`(9x+3y^2)dy/dx = 2x-9y`

`dy/dx = (2x-9y)/( 3(3x+y^2))`