Question: Differentiate matrix and create a function

Hi everyone,

 

I am trying to understand how can I create a function based on the differentiate of a matrix.

 

For instance:
 

And I would like to create the matrix FF based on the derivative of F with respect to x and then be able to use FF and a function.

I tried to combine, unapply, map and diff but I can't reach what I'm looking for.

Do you guys have any ideas?

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