The derivative with respect to 'x' is 4y3 . The derivative with respect to 'y' is 12xy2 .
(x+y)4 = (x2+2xy+y2)2 = x4+4x3y+6x2y2+4xy3+y4
You can't exactly FOIL it because you don't have a problem in the form of (3x + 2)(4x - 6) Frankly, I don't understand exactly what question you are trying to solve, so I'll give you a couple of examples that might help. (-y32) times (2y - 4xy2) turns into: ((-1)(y32) times 2y) plus ((-1)(y32) times ((-1)(4xy2)) which becomes -2y33 plus 4xy34 which would be more often expressed as 4xy34 - 2y33 Perhaps you meant something more like this: (-y times 32) times (2y - 4xy2) turns into: (-32y) times (2y - 4xy2) which becomes (-y times 2y) + (-y times -4xy2) + (32 times 2y) + (32 times -4xy2) which becomes -2y2 + 4xy3 + 64y - 128xy2 which is 4xy3 -128 xy2 - 2y2 + 64y I'm sure if I'm gotten it wrong, someone will straighten it out. Also, if this doesn't help, please fix up the original question so it can be answered properly.