2
SOLUTION 1 Begin with x 3 y 3 = 4 Differentiate both sides of the equation, getting D ( x 3 y 3) = D ( 4 ) , D ( x 3) D ( y 3) = D ( 4 ) , (Remember to use the chain rule on D ( y 3) ) 3x 2 3y 2 y' = 0 , so that (Now solve for y' ) 3y 2 y' = 3x 2, and Click HERE to return to the list of problems SOLUTION 2 Begin with (xy) 2 = x y 1 Differentiate both sidesValue (x y)3 (y z)3 (z x)3 is (1) (x y)3 (y z)3 (z x)3 (2) 3 (x y) y3 z3 3xyz (4) x3 y3 z3 2x2y 2y2z 2z2x
