Question: How can I calculate the Frechet derivative in maple ?

For the function


F(u)= u(x)u(y)                    


the first Frechet derivative is given as


F'(u)v = v(x)u(y) + u(x)v(y)

that is the Frechet derivative of F(u) acting on v.


So how do I get maple to give me the Frechet derivative of  F(u)= u(x)u(y)  ?

F(u)=u(x)u(y) just means that at one stage u depends on x then at another stage it depends on y. Here both stages are interacting but I state this just as background information in case you wondered.

The Frechet derivative is with respect to a point (function) v and not x or y upon which u depends. So it is the derivatibve of F(u)= u(x)u(y)  at v given as above is what I am after in Maple. I can do it by hand but how do I get Maple to do it? 


Also if you have an alternative way of computing this derivative I would welcome your advice.

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