symbolic differentiation is SO EASY in haskell!

symdiff.hs

-- i mean, this is basically just a high school formula sheet
-- that happens to also be valid haskell
-- (we're differentiating against "Symbol")

diff (Symbol) = Val 1
diff (Neg x) = Neg (diff x)
diff (Add x y) = Add (diff x) (diff y)
diff (Mul x y) = Add (Mul (diff x) y ) (Mul x (diff y))
diff (Sub x y) = diff (Add x (Neg y))
diff (Pow x (Val n)) = Mul (Val n) (Pow x (Val (n - 1) ) )
diff (Div x y) = diff (Mul x (Pow y (Val (-1)) ) )
diff (Exp x) = Mul (Exp x) (diff x)
diff (Sin x) = Mul (Cos x) (diff x)
diff (Cos x) = Neg (Mul (Sin x) (diff x) )
diff (Fxn xs y) = Mul (Fxn (xs ++ "\'") y) (diff y)

-- most of this stuff is written in polish notation, but if we want to be even clearer
-- we can write it in infix notation:
diff (x `Mul` y) = ((diff x) `Mul` y ) `Add`  (x `Mul` (diff y))

Do you have the part for the codes Add, Pow and Mul?