HP 50g Graphing Calculator - Manual (Page 442)

Page 13-7
Derivatives of equations
You can use the calculator to calculate derivatives of equations, i.e., expressions
in which derivatives will exist in both sides of the equal sign. Some examples
are shown below:
Notice that in the expressions where the derivative sign ( ∂) or function DERIV
was used, the equal sign is preserved in the equation, but not in the cases
where function DERVX was used. In these cases, the equation was re-written
with all its terms moved to the left-hand side of the equal sign. Also, the equal
sign was removed, but it is understood that the resulting expression is equal to
zero.
Implicit derivatives
Implicit derivatives are possible in expressions such as:
Application of derivatives
Derivatives can be used for analyzing the graphs of functions and for
optimizing functions of one variable (i.e., finding maxima and minima). Some
applications of derivatives are shown next.