Question: Is Maple able to do this workout?

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

 

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