(DEFUN DIFF-POL (DT DX)
  (COND ((NULL DT) NIL)
        ((ATOM DT) (DIFF-POL-ATOM DT DX))
        ((AND (LISTP DT) (EQL (CAR DT) '-)) (DIFF-POL-ATOM (CADR DT) DX))
        ((AND (LISTP DT) (EQL (CAR DT) '*)) (DIFF-POL-PROD (CADR DT) (CADDR DT) DX))
        ((AND (LISTP DT) (EQL (CAR DT) 'EXPT)) (DIFF-POL-EXPT (CADR DT) (CADDR DT) DX))
        ((AND (LISTP DT) (EQL (CAR DT) '+)) (DIFF-POL-SUMME (CDR DT) DX))
        (T NIL)
  )
)

(DEFUN DIFF-POL-ATOM (DT DX)
  (COND ((EQL DT DX) 1)
        (T 0)
  )
)

(DEFUN DIFF-POL-PROD (KO V DX)
  (COND ((EQL V DX) KO)
        ((LISTP V) (LIST '* KO (DIFF-POL V DX)))
        (T 0)
  )
)

(DEFUN DIFF-POL-EXPT (V EXP DX)
  (COND ((NOT (EQL V DX)) 0)
        ((NOT (NUMBERP EXP)) (LIST '* EXP (LIST 'EXPT V (LIST '- EXP 1))))
        ((= EXP 1) 1)
        ((= EXP 2) (LIST '* '2 V))
        (T (LIST '*  EXP (LIST 'EXPT V (- EXP 1) )))
  )
)

(DEFUN DIFF-POL-SUMME (DT DX)
  (COND ((= (LENGTH DT) 1) (DIFF-POL (CAR DT) DX))
        (T (CONS '+ (DIFF-POL-SUMME-R DT DX)))
  )
)

(DEFUN DIFF-POL-SUMME-R (DT DX)
  (COND ((NULL DT) NIL)
        ((AND (NUMBERP (DIFF-POL (CAR DT) DX)) (= (DIFF-POL (CAR DT) DX) 0)) (DIFF-POL-SUMME-R (CDR DT) DX))
        (T (CONS (DIFF-POL (CAR DT) DX) (DIFF-POL-SUMME-R (CDR DT) DX)))
  )
)
(DIFF-POL 1 'X);->0