Differentiation - HP -28S Quick Reference

than the specified accuracy of 1E-3.
In case the returned upper limit for the relative error is negative then
the integral did not converge.
The function to integrate may also be specified as a program which
evaluates the integration variable and returns the function result on the
stack. No value must be taken from the stack:
<<x EXP 5 +>> {'x' 1 2} 1E-3 ∫ returns 9.67 0.01.
Numeric Example: <<EXP 5 +>> {1 2} 1E-3 ∫ returns 9.67 0.01.
integration • Stack level 3 must contain a program (or the name of a variable
with implicit
containing a program). The program implements the function to
integration integrate and it must take one argument from the stack and return a
variable
single real result on the stack.
• Stack level 2 contains a list which specifies the lower and upper limits of
integration (real values).
• Stack level 1 contains the desired absolute accuracy of the result.
General The differentiation symbol ∂ (d/dx located on the "6" key) can perform
symbolic differentiation of a very wide range of functions. Ie. many
built-in functions of the HP-28S can be differentiated.
In addition it is possible to specify derivatives for user-defined
functions which the differentiation algorithm will use to generate
complete differentials.
Complete Invoked by issuing the ∂ command explicitly.

differentiation

Example: 'SIN(2*X)+X^2' 'X' ∂ results in 'COS(2*X)*2+2*X'.
If the variable X exists the result will be the differential evaluated at
position X. An error occurs if X contains an improper object (ie. a list).
Partial Invoked by using ∂ in an expression.
differentiation Example: '∂X(SIN(2*X)+X^2)' EVAL results in
'∂X(SIN(2*X))+∂X(X^2)'. The next EVAL will return
'COS(2*X)*∂X(2*X)+∂X(X)*2*X^(2-1)' and then
'COS(2*X)*(2*∂X(X))+2*X' and finally
'COS(2*X)*2+2*X'.
After this EVAL won't change the result any more.
If necessary, use COLCT to simplify the resulting expression.
User functions A user defined function or a program in functional form can be
differentiated as well. Example: First create a function F(x,y) that takes
two arguments: <<→ a b 'a*b + a + b' >> 'F' STO
Then differentiate d/dx F(x,x+2): 'F(X,X+2)' 'X' ∂ .
The result is: 'X+2+X+1+1' and after COLCT '4+2*X'.
Note that the program given above must contain an expression in
single quotes. It cannot contain another program in <<>> brackets
even though these kinds of program can be invoked in functional
notation, see Programs.
User-defined Not all built-in functions can be differentiated symbolically.
differentials Example: '%(100,3)' is the functional notation of % and returns 3%
of 100. '%(X,3)' 'X' ∂ returns 'der%(X,3,1,0)' because the
derivative of % is not known.
HP-28S
Differentiation
44