Derivatives
Use the Axiom function D to differentiate an
expression.
To find the derivative of an expression f with respect to a variable x,
enter D(f,x).
An optional third argument n in D asks Axiom for
the nth derivative of f. This finds the fourth derivative of f with
respect to x.
You can also compute partial derivatives by specifying the order of
differentiation.
Axiom can manipulate the derivatives (partial or iterated) of expressions
involving formal operators. All the dependencies must be explicit. This
returns 0 since F (so far) does not explicitly depend on x.
Suppose that we have F a function of x, y, and z, where x and y are
themselves functions of z. Start by declaring that F, x, and y are
operators.
You can use F, x, and y in expressions.
Differentiate formally with respect to z. The formal derivatives appearing
in dadz are not just formal symbols, but do represent derivatives of x, y, and
F.
You can evaluate the above for particular functional values of F, x, and y.
If x(z) is exp(z) and y(z) is log(z+1), then this evaluates dadz.
You obtain the same result by first evaluating a and then differentiating.
