# Complete Differentiation; Integrating An Expression - HP -28S Manual

Complete
Differ~ntiation
To differentiate an expression all at once, perform differentiation as a
stack operation. Again, suppose you want to find:
..!L
tan
(x
2
+
1)
dx
Put the expression to be differentiated on the stack.
. 1
CLEAR
I
3:
2:
CJ
TAN
X.~ 2 ~
1
1
ENTER
I
1 :
' TAN
(W'2+
1 ) ,
RI:IImrnaallEmlllil3llllllCl
Specify the variable of differentiation.
CJ
X
1
ENTER
I
r:::
3 : - : : " : - - - - - - - - - - - - ,
2:
'TAN(X
A
2+1),
1:
'X'
RI:IImrnaallEmlllil3llllllCl
Differentiate the expression .
1
d/dx
I
The fully evaluated derivative is returned to level 1.
Integrating an Expression
The HP-28S calculates the indefinite integral of an expression by
sym-
bolic integration, which returns an expression as a result. This method
returns an exact result only for polynomial expressions. (For other ex-
pressions, the HP-28S integrates a Taylor series approximation to the
expression. See "Calculus" in the Reference Manual for details.) The
first example below demonstrates symbolic integration.
In contrast, definite integrals are calculated by
numerical integration,
which returns numerical results. This method works for any expres-
sion that is "well-behaved" in the mathematical sense. The second
example below demonstrates numerical integration.
120
10: Calculus  