HP 48G - And Differentiation

(3) AND DIFFERENTIATION
To take a derivative, use D'if ferent iate..,
(under (2)SYMBOLIC)) or the command & (via (=)3)).
Numerical Differentiation
Example: Find the slope of 1/xat x=2.7183. Press (D)
(symsoLic), then selectD'it f erent i at e.. Enter
the EXPE: ('] 1]=]a]X]([ENTER]. Specify the variable in
Yak: (o)X)ENTER). SetkEsULT: toMumer1c (use
if needed); and intheYALUE: field, enter(2] - 7] 1] 8] 3).
Now press IFL[HM. Result: —.1353....
@ can do the same thing on the stack: First, enter the
expression ('1-¥' here), then the variable, ('’
here). And for a numeric derivative, store the value in
#: (7GR ETER(@)(XISTO). Press (2)3).
Symbolic Differentiation
Example: Find the slope of 1/x at any point. First for
a symbolic derivative, you purge the variable name—
'%' here (and you must do this throughout the cur-
rent path): (*Jo)x]&JPURG). Then proceed: Press()
and select'if ferent 1ate... Enter
the EXPR: (" [1)=]o)(X)ENTER). Put the variable in ¥k:
(@]X)ENTER). SetkEsULT: to Sumbiol i (use if
needed). Press IN[E. Result: '-(1<8*Z)"
& does the same thing on the stack: Enter the expres-
sion ('1-1"), the variable, ('#'), and press (=]3).
Stepwise Differentiation
Example: Find the slope of (sin x)/x at any point.
First, for a symbolic derivative, you must purge the
variable name, '#' ("JoJX]<JPURG)—and you must
do this throughout the current path. Next, set FAD
mode (if it's not set already). Now press
and select it f erent iate.. Next, enter the
EXPE: (" JSIN o] X)(» X]JENTER); then put the variable
of differentiation (+4) into ¥ak: (a]X)ENTER). Finally, set
RESULT: to'Sumbio 1 1C (use(+/5)ifnecessary). Now,
at this point, instead of pressing (which would
do the complete differentiation), press BT ...
Result: 'dHCSINCE)Y 1H=-SINCH I #aR (1 B2
Now just press repeatedly to see each step in
the differentiation.
(@) and Differentiation 23