(defmacro deriv
  "Macro for symbolic differentiation. with 2 args, takes 1st degree deriv.
  with 3, takes arbitrary degrees. contains all deriv rules for basic funcs.


  Examples:

    (use '(incanter core symbolic))

    (deriv (+ x 3) x) ; => 1
    (deriv (* x y) x) ; => y
    (deriv (* (* x y) (+ x 3)) x) ; => (+ (* (+ x 3) y) (* x y))
    (deriv (* (* x y) (+ x 3)) y) ; => (* (+ x 3) x)

    (deriv (* x y (+ x 3)) x) ; => (+ (* y (+ x 3)) (* y x))
    (deriv (* x y (+ x 3)) y) ; => (* (+ x 3) x)

    (deriv (sin x) x) ; => (cos x)
    (deriv (cos x) x) ; => (* -1 (sin x))

    (deriv (sin (* x y)) y) ; => (* x (cos (* x y)))

    (deriv (pow x 3) x) ; => (* 3 (pow x 2))
    (deriv (** x 3) x) ; => (* 3 (pow x 2))

    (deriv (pow x 3) x 2) ; => (* 3 (* 2 x))

    (deriv (* x y (+ x 3)) x 2) ; => (+ y y)
    (deriv (* x y (+ x 3)) x 3) ; => 0

    (deriv (+ (* 3 x) (* 8 x)) x) ; => 11



    ;; NOT WORKING YET

    (deriv (/ 1 x) x) ; => (* (deriv* (* (x)) x) (* -1 (pow (* (x)) -2)))
                                          ^-- need to fix
"
  ([exp v]
     `(deriv* '~exp '~v))
  ([exp v degree]
     `(deriv* '~exp '~v ~degree)))