1  REM  ****  HP BASIC PROGRAM LIBRARY  *******************************
2  REM
3  REM        DERTIV:   COMPUTER-AUGMENTED CALCULUS TOPICS
4  REM
5  REM        36662 REV  A   10/73
6  REM
7  REM  ****  CONTRIBUTED PROGRAM  ************************************
100  PRINT "THIS PROGRAM WILL COMPUTE A SET OF APPROXIMATIONS"
110  PRINT "TO THE DERIVATIVE OF ANY FUNCTION F(X) WHICH YOU GIVE"
120  PRINT "IT FOR ANY VALUE YOU ASSIGN TO THE INDEPENDANT "
130  PRINT "VARIABLE X, PROVIDED THE FUNCTION HAS A DERIVATIVE"
140  PRINT "FOR THAT X."
150  PRINT 
160  PRINT "FOR EACH X YOU WILL GET AS OUTPUT THE VALUES OF X"
170  PRINT "AND F(X), AS WELL AS A SET OF APPROXIMATIONS TO"
180  PRINT "F'(X) FOR H= .1, -.1, .01, -.01, .001, -.001, "
190  PRINT ".0001, AND -.0001."
200  PRINT 
210  PRINT 
220  PRINT 
230  PRINT "WHAT IS X";
240  INPUT X
250  PRINT 
260  PRINT "        H       APPROXIMATION TO F'(X)"
270  FOR N=1 TO 4
280  LET H=1/10^N
290  LET C=0
300  LET I=0
310  LET A=X
320  LET X=X+H
330  LET Y=EXP(X)
340  IF I=1 THEN 390
350  LET I=I+1
360  LET D1=Y
370  LET X=A
380  GOTO 330
390  LET D2=Y
400  LET D=(D1-D2)/H
410  PRINT H,D
420  LET C=C+1
430  IF C=2 THEN 460
440  LET H=(-H)
450  GOTO 300
460  PRINT 
470  NEXT N
480  PRINT 
490  PRINT 
500  PRINT "X = ";A;" Y = ";D2
510  GOTO 210
520  END 
530  CHAIN "SYSTEM"
540  END 
