Question

How do you differentiate `4x^2 +3y^2 -2xy = 32`?

Answer 1

`y'=((y-4x))/((3y-x))`

Explanation:

`4x^2+3y^2-2xy=32`

To solve this we use implicit differentiation:

`D(4x^2+3y^2-2xy)=D(32)`

`8x+6yy'-2(xy'+y)=0`

Now solve for y'`rArr`

`8x+6yy'-2xy'-2y=0`

`8x+y'(6y-2x)-2y=0`

`y'(6y-2x)-2y=-8x`

`y'(6y-2x)=2y-8x`

`y'=((2y-8x))/((6y-2x))`

`y'=(cancel(2)(y-4x))/(cancel(2)(3y-x))`

`y'=((y-4x))/((3y-x))`