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

1 Answer
Jun 27, 2015

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))