## (“Derivative”)

Keyboard Access: f(x) 'x' f'(x) 'x(f(x))' EVAL stepwise chain rule of differentiation (HP-28/48)HP48: RS-SIN HP49/50: RS-COSDerivative 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”) ofat 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 representsvelocity(feet per second, the rate at which thepositionis changing), and representsacceleration(feet per second squared, the rate at which thevelocityis changing).Simple example: If , what is ?

This means two things:

(a) if you plot the X^{2}parabola, you’ll see that the slope at each point on the parabola is exactly twice the value of X; and

(b) if X^{2}represents thepositionof something (e.g. how many feet an object has fallen in x seconds) then thevelocitywill be twice the elapsed time (2X).And what is ? (Assuming that is still on stack level 1.)

2

This means that theaccelerationis 2 feet per second squared.

HP-28/48only: 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.

HP49/50only: Contrary to HP’s documentation, doesnotordinarily 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 onStep-by-step Mode (set flag -100).See for more information about derivatives in general.

The

HP49/50offers a command for ease of use of der.BYTES: 2.5