:-op(300,yfx,^).

d(X,X,1):-!.
d(C,X,0):-atomic(C).
d(-U,X,-A):-d(U,X,A).
d(U+V,X,A+B):-d(U,X,A),d(V,X,B).
d(U-V,X,A-B):-d(U,X,A),d(V,X,B).
d(C*U,X,C*A):-atomic(C), \+ C=X, d(U,X,A),!.
d(U*V,X,B*U+A*V):-d(U,X,A),d(V,X,B).
d(U/V,X,A):-d(U*V^(-1),X,A).
d(U^C,X,U^(C-1)*W):-atomic(C),\+ C=X,d(U,X,W).
d(log(U),X,A*U^(-1)):-d(U,X,A).