HP 48g Graphing Calculator - Manual (Page 252)

Implicit Differentiation
An implicit function of, say, x and y is a function in which one of the
variables (y ) is not directly expressed in terms of the other variable
(/). This may be because it is either impossible, difficult, or not at all
obvious how the expression may be solved for one variable in terms
of the other. When this happens it is still possible to differentiate the
expression using normal rules of differentiation (and the chain rule).
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To perform implicit differentiation:
1. Enter the implicit function onto the stack. Instead of using two
independent variables (such as x and y), make the second variable
dependent on the first (such as x and y(x)). This links the two
variables appropriately so that the differentiation treats the
function as implicit, instead of eliminating one of the variables as a
constant.
2. Enter the variable of differentiation onto the stack (using the '
delimiters).
3. Press OCD to compute the implicit derivative. You may see a
user-defined derivative (such as derYO-i? 1)) included in the result.
This is the way the HP 48 expresses the derivative of one variable
dY '
with respect to the other (such as
Taylor Polynomial Approximation
For any mathematical function represented by a symbolic expression,
you can compute a Taylor’s polynomial approximation about r = 0,
sometimes called a Maclaurin series. You can also specify the order of
the polynomial.
1. Press fT^fSYMBOLIC 1 ffl (T)
POLYHuMIflL form.
OK to open the I' h VLON
20-12 Calculus and Symbolic Manipulation