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The Compleat User RPL Encyclopedia


(“Derivative”)

f(x)  'x'    f'(x)
'x(f(x))'  EVAL    stepwise chain rule of differentiation (HP-28/48)
Keyboard Access:
   HP48: RS-SIN
HP49/50: RS-COS
Derivative Function: Takes the derivative of an expression, number, or unit object with respect to a specified variable of differentiation.

The derivative of function  is symbolically written as  and represents the slope (“rate of change”) of at all values of x.

The derivative of  is called the “second derivative” of , is symbolically written as , and represents the rate at which that rate of change is changing.

Example: If  represents position (say, feet) at time t (say, seconds), then  represents velocity (feet per second, the rate at which the position is changing), and  represents acceleration (feet per second squared, the rate at which the velocity is changing).

Simple example: If , what is  ?
    
This means two things:
(a) if you plot the X2 parabola, you’ll see that the slope at each point on the parabola is exactly twice the value of X; and
(b) if X2 represents the position of something (e.g. how many feet an object has fallen in x seconds) then the velocity will be twice the elapsed time (2X).

And what is  ? (Assuming that is still on stack level 1.)
    2
This means that the acceleration is 2 feet per second squared.

HP-28/48 only: If  is used in its algebraic notation, then executing performs only one step of chain rule differentiation.  must be repeated until no  symbols are left to achieve the actual derivative. To get the final derivative in one step, use the stack syntax of  instead of the algebraic syntax.

HP49/50 only: Contrary to HP’s documentation,  does not ordinarily perform only one step of chain rule differentiation when used in its algebraic notation.  returns the final derivative, just like , when flag -100 is clear (default). To perform stepwise differentiation, turn on Step-by-step Mode (set flag -100).

See for more information about derivatives in general.

The HP49/50 offers a command for ease of use of der.

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