derivative function

derivative.hs

derivative :: (Num a) => Expr a -> Expr a
derivative (Var c)           = Const 1
derivative (Const x)         = Const 0
--product rule (ab' + a'b)
derivative (a :*: b)         = (a :*: (derivative b)) :+:  (b :*: (derivative a)) -- product rule
 --power rule (xa^(x-1) * a')
derivative (a :^: (Const x)) = ((Const x) :*: (a :^: (Const $ x-1))) :*: (derivative a)
derivative (a :+: b)         = (derivative a) :+: (derivative b)
 -- quotient rule ( (a'b - b'a) / b^2 )
derivative (a :/: b)         = ((derivative a :*: b) :+: (negate' (derivative b :*: a))) 
                               :/: 
                               (b :^: (Const 2))
derivative expr              = error "I'm not a part of your system!" -- unsupported operation