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