MATHLAB

COMMENT MATHLAB program to differentiate polynomials;

PROCEDURE DIFF(EXPR, VAR);
BEGIN
  COMMENT Differentiate EXPR with respect to VAR;
  IF ATOM(EXPR) THEN
    IF EXPR = VAR THEN RETURN 1
    ELSE RETURN 0
  ELSE IF CAR(EXPR) = PLUS THEN
    RETURN CONS(PLUS, MAPCAR(LAMBDA(X, DIFF(X, VAR)), CDR(EXPR)))
  ELSE IF CAR(EXPR) = TIMES THEN
    COMMENT Product rule: d(uv)/dx = u*dv/dx + v*du/dx;
    BEGIN
      SCALAR U, V;
      U := CAR(CDR(EXPR));
      V := CAR(CDR(CDR(EXPR)));
      RETURN CONS(PLUS,
        LIST(CONS(TIMES, LIST(U, DIFF(V, VAR))),
             CONS(TIMES, LIST(V, DIFF(U, VAR)))))
    END
  ELSE IF CAR(EXPR) = EXPT THEN
    COMMENT Power rule: d(x^n)/dx = n*x^(n-1);
    BEGIN
      SCALAR BASE, EXP;
      BASE := CAR(CDR(EXPR));
      EXP := CAR(CDR(CDR(EXPR)));
      RETURN CONS(TIMES,
        LIST(EXP,
             CONS(EXPT, LIST(BASE, CONS(PLUS, LIST(EXP, -1)))),
             DIFF(BASE, VAR)))
    END
END;

COMMENT Test the differentiation;
EXPR1 := CONS(EXPT, LIST(X, 3));
PRINT("d/dx(x^3) =", DIFF(EXPR1, X));

EXPR2 := CONS(TIMES, LIST(X, CONS(EXPT, LIST(X, 2))));
PRINT("d/dx(x*x^2) =", DIFF(EXPR2, X));