Question

How do you implicitly differentiate `15=x^2/y+y^2`?

Answer 1

`dy/dx=[2x]/[15-3y^2]`

Explanation:

`15=x^2/y +y^2` , Multiply both sides by `y`

`15y=x^2+y^3` and so differentiating implicitly with respect to `x`

`15dy/dx=2x+3y^2dy/dx`

`15dy/dx-3y^2dy/dx=2x`

`dy/dx[15-3y^2]=2x`

`dy/dx=[2x]/[15-3y^2]`.