HP 48g Graphing Calculator - Manual (Page 251)

Creating User-Defined Derivatives
If you execute d for a function that has no built-in derivative, d
returns a new function whose name is der followed by the original
function name. The new function has arguments that are the
arguments of the original function, plus the arguments’ derivatives.
(You can differentiate further by creating a user-defined function to
represent the new derivative function.)
If you execute d for a formal user function (a name followed by
arguments in parentheses, for which no user-defined function exists
in user memory), d returns a formal derivative whose name is der
followed by the original user function name, plus the arguments and
their derivatives.
Example: The HP 48 definition of % does not include a derivative.
If you enter ' dZ<“;;<Xj Y) > ' and press fEVAll. you get
' der”;;
, i :
J5ach argument of the % function results in two arguments
for the der% function—K results in Y and dZCK), and V
results in
Y
and
d Z < Y > ,
To define the derivative function for %, you can enter
' d e r K X f y |i d ? d y > = < x * d y+y * d 10 9 ' and press
(DW^. DERZ will appear in your ’VAR menu.
Now you can obtain the derivative of ' % < X, > '
by entering the expression and the variable ' Y ' , then
pressing 0(D i^fALGEBRAl CuLCT. The result is
20
Example: Enter the derivative of a formal user function,
' <xl ;i x £ h : k 3> ) '. Then evaluate it by pressing
fEVAL~). The result is this:
' d 0 r f (. ;:< I j ;:-iX
, ,
,::Jx i.
1 ~
<3X K X',d ) d;:-i t '
Calculus and Symbolic Manipulation 20-11