d(X, X, 1).
d(Y, _, 0) :- atomic(Y).
d(A + B, X, DA + DB) :-
d(A, X, DA),
d(B, X, DB).
d(A - B, X, DA - DB) :-
d(A, X, DA),
d(B, X, DB).
d(A * B, X, A * DB + B * DA) :-
d(A, X, DA),
d(B, X, DB).
d(A / B, X, ( DA * B - A * DB ) / B * B) :-
d(A, X, DA),
d(B, X, DB).

d(sin(A), X, DA * cos(A) ) :-
	d(A, X, DA).
d(A ^ B, X, A ^ (B) * ln(A)) :-
	d(A, X, DA).
(wykładnicza) d(A ^ X, X, ln(A) * A ^ X ).