D ( x3 + y3 ) = D ( 4 ) ,
D ( x3 ) + D ( y3 ) = D ( 4 ) ,
(Remember to use the chain rule on D ( y3 ) .)
3x2 + 3y2 y' = 0 ,
so that (Now solve for y' .)
3y2 y' = - 3x2 ,
and
$ y' = \displaystyle{ - 3x^2 \over 3y^2 } = \displaystyle{ - x^2 \over y^2 } $
