PROGRAM 8


;  FILENAME:  PROGRAM8.LSP      AUTHOR:  ANTHONY F. ORTIZ

;  SYMBOLIC DIFFERENTIATION PROGRAM
(DEFUN DERIV (U X)
    (COND
        ;  RULES 1 AND 2:  D/DX (X) AND D/DX (C)
        ((ATOM U) (IF (EQ U X) 1 0))
        ;  RULES 3 AND 4:  D/DX (F + G) AND D/DX (F - G)
        ((OR (EQ (FIRST U) '+) (EQ (FIRST U) '-))
            (LIST (FIRST U) (DERIV (SECOND U) X) (DERIV (THIRD U) X)))
        ;  RULE 5:  D/DX (F * G)
        ((EQ (FIRST U) '*)
            (LIST '+
            (LIST (FIRST U) (THIRD U) (DERIV (SECOND U) X))
            (LIST (FIRST U) (SECOND U) (DERIV (THIRD U) X))))
        ;  RULE 6:  D/DX (F / G)
        ((EQ (FIRST U) '/)
            (LIST '/
            (LIST '-
            (LIST '* (THIRD U) (DERIV (SECOND U) X))
            (LIST '* (SECOND U) (DERIV (THIRD U) X)))
            (LIST '* (THIRD U) (THIRD U))))
        ;  RULE 7:  THE CHAIN RULE, I.E. D/DX (F ^ N)
        ((EQ (FIRST U) '^)
            (LIST '*
            (LIST '* (THIRD U)
            (IF (EQ (THIRD U) 2) (SECOND U)
                (LIST (FIRST U) (SECOND U)
                (- (THIRD U) 1))))
                (DERIV (SECOND U) X)))
        ;  RULE 8: D/DX LN (F(X) = 1 / F(X) * F'(X)
        ((EQ (FIRST U) 'LN)
            (LIST '*
            (LIST '/  '1 (SECOND U))
            (DERIV (SECOND U) X)))                        
            (T NIL)))

;  OUTFILE:  PROG8.OUT

XLISP version 2.0, Copyright (c) 1988, by David Betz
; loading "init.lsp"
> (load "program8.lsp")
; loading "program8.lsp"
T
> (deriv '(^ x 3) 'x)
(* (* 3 (^ X 2)) 1)
>




BACK TO CS3120 PAGE.