User Manual

184 Symbols
d() (derivative)
Catalog >
d(Expr1, Var[, Order]) | Var=Value ⇒
value
d(Expr1, Var[, Order]) ⇒ value
d(List1, Var[, Order]) ⇒ list
d(Matrix1, Var[, Order]) ⇒ matrix
Except when using the first syntax, you
must store a numeric value in variable Var
before evaluating d(). Refer to the
examples.
d() can be used for calculating first and
second order derivative at a point
numerically, using auto differentiation
methods.
Order, if included, must be=1 or 2. The
default is 1.
Note: You can insert this function from the
keyboard by typing derivative(...).
Note: See also Firstderivative, page 5 or
Secondderivative, page 5.
Note: The d() algorithm has a limitation: it
works recursively through the unsimplified
expression, computing the numeric value of
the first derivative (and second, if
applicable) and the evaluation of each
subexpression, which may lead to an
unexpected result.
Consider the example on the right. The first
derivative of x•(x^2+x)^(1/3) at x=0 is equal
to 0. However, because the first derivative
of the subexpression (x^2+x)^(1/3) is
undefined at x=0, and this value is used to
calculate the derivative of the total
expression, d() reports the result as
undefined and displays a warning message.
If you encounter this limitation, verify the
solution graphically. You can also try using
centralDiff().