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

I was told that the following workout was done in Maple.  I have tried to read material about how to do it but I am completely lost.  Can someone indicate me where I can read in oder to do what the image says or give me some tips please?  

where all functions are dependent on the variables (u,v).

Observation: subscripts means partial derivatives of the function while superscripts are just for naming different functions,i.e Gamma^1 and Gamma^2 are two functions.

Sergio

Sergio