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Question: How do I define a function in terms of unknown functions

Question:How do I define a function in terms of unknown functions

Lightkage 15 Maple
derivative procedure
October 03 2017
1

I was to define a function of two variable in terms of two other functions.  This other function depends on another two functions which are unknown.  For example

g(u,v)=alpha(u,v)*beta(u,v)

h(u,v)=alpha(u,v)+beta(u,v)

f(u,v) = D_1g(u,v)*h(u,v).

 

I tried by writtinge this line 

g:=(u,v)->alpha(u,v)*beta(u,v)

h:=(u,v)->alpha(u,v)+beta(u,v)

f:=(u,v)->D[1](g)(u,v)*h(u,v).

Is this correct?   

If this is correct, then how I make maple show f in tems of the unkown functions alpha and beta?

 

Thanks,

 

Sergio
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