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.