reduce (Deriv (EPoly (PowerOf X 1))) = EPoly (C 1)
reduce (Deriv (EPoly (PowerOf X 2))) = EPoly (PolyMult 2 X)
reduce (Deriv (EPoly (PowerOf X c))) = EPoly (PolyMult (toRational(c)) (PowerOf X (c-1)))
reduce (Deriv (Sin (EPoly X))) = Cos (EPoly X)
reduce (Deriv (Sin (EPoly (PowerOf X 0)))) = EPoly (C 0)
reduce (Deriv (Sin (EPoly (PowerOf X 1)))) = Cos (EPoly X)
reduce (Deriv (Sin (EPoly (PowerOf X c)))) = ExpMult (EPoly (PolyMult (toRational(c)) (PowerOf X (c-1)))) (Cos (EPoly (PowerOf X c)))
reduce (Deriv (Cos e)) = ExpMult (EPoly (C (-1))) (Sin e)
reduce (Deriv (ExpMult (EPoly (C (-1))) (Sin e))) = ExpMult (EPoly (C (-1))) (Cos e)
reduce (Deriv (ExpMult (EPoly (C (-1))) (Cos e))) = ExpMult (EPoly (C (-1))) (Sin e)
reduce (Deriv (ExpPlus x y)) = (ExpPlus (reduce(Deriv x)) (reduce(Deriv y)))
reduce (Deriv (Deriv y)) =reduce(Deriv (reduce(Deriv y)))
reduce (Deriv (ExpMult x y)) = (ExpMult (reduce(Deriv x))  (reduce(Deriv y)))
reduce (Deriv (EPoly (C (-1)))) = EPoly (C 0)
reduce (Deriv (EPoly (C 1))) = EPoly (C 0)
reduce (Deriv (EPoly (C 0))) = EPoly (C 0)
reduce (Deriv (EPoly X)) = EPoly (C 1)
reduce (Deriv (EPoly (PolyPlus X X))) = EPoly(C 2)
reduce (Deriv (EPoly (PolyMult x X))) = EPoly(C 0)
reduce (Deriv (EPoly (PolyPlus X c))) = EPoly(C 1)
reduce (Deriv (EPoly (PolyPlus c1 c2))) = EPoly(C 0)
reduce (Deriv (EPoly (C p))) = EPoly(C 0)
reduce (Deriv (EPoly (PolyMult x (C y)))) = EPoly (C (y*x))