Question

How do you differentiate `y^2-y=3x^2y-6x+3`?

Answer 1

`dy/dx=(6xy-6)/(2y-1-3x^2)`

Explanation:

differentiate all terms `color(blue)"implicitly with respect to x"`

Note that `3x^2y` has to be differentiated using the `color(blue)"product rule"`

`2y.dy/dx-1.dy/dx=(3x^2.dy/dx+y.(6x))-6+0`

`rArr2ydy/dx-dy/dx-3x^2dy/dx=6xy-6`

`rArrdy/dx(2y-1-3x^2)=6xy-6`

`rArrdy/dx=(6xy-6)/(2y-1-3x^2)`