(define uprosc
    (lambda (w)
        (cond
            ((not (pair? w))
                w)
            ((equal? (cadr w) '+)
                (let ((wl (uprosc (car w))) (wr (uprosc (caddr w))))
                    (cond
                        ((equal? wl 0) wr)
                        ((equal? wr 0) wl)
                        ((and (number? wr) (number? wl)) (+ wl wr))
                        (else (list wl '+ wr)))))
            ((equal? (cadr w) '-)
                (let ((wl (uprosc (car w))) (wr (uprosc (caddr w))))
                    (cond
                        ((equal? wr 0) wl)
                        ((and (number? wr) (number? wl)) (- wl wr))
                        (else (list wl '- wr)))))
            ((equal? (cadr w) '*)
                (let ((wl (uprosc (car w))) (wr (uprosc (caddr w))))
                    (cond
                        ((equal? wl 0) 0)
                        ((equal? wr 0) 0)
                        ((equal? wl 1) wr)
                        ((equal? wr 1) wl)
                        ((and (number? wr) (number? wl)) (* wl wr))
                        (else (list wl '* wr)))))
            ((equal? (cadr w) '/)
                (let ((wl (uprosc (car w))) (wr (uprosc (caddr w))))
                    (cond
                        ((equal? wl 0) 0)
                        ((equal? wr 1) wl)
                        ((and (number? wr) (number? wl)) (/ wl wr))
                        (else (list wl '/ wr)))))
            (else w))))

(define pochodna
    (lambda (w x)
        (uprosc
            (cond
                ((equal? w x)
                    1)
                ((not (pair? w))
                    0)
                ((equal? (cadr w) '+)
                    (list
                        (pochodna (car w) x)
                        '+
                        (pochodna (caddr w) x)))
                ((equal? (cadr w) '-)
                    (list
                        (pochodna (car w) x)
                        '-
                        (pochodna (caddr w) x)))
                ((equal? (cadr w) '*)
                    (list
                        (list
                            (pochodna (car w) x)
                            '*
                            (caddr w))
                        '+
                        (list
                            (car w)
                            '*
                            (pochodna (caddr w) x))))
                ((equal? (cadr w) '/)
                    (list
                        (list
                            (list
                                (pochodna (car w) x)
                                '*
                                (caddr w))
                            '-
                            (list
                                (car w)
                                '*
                                (pochodna (caddr w) x)))
                        '/
                        (list
                            (caddr w)
                            '*
                            (caddr w))))
                (else 'error)))))

(pochodna '((x + a) * (x + b)) 'x)