Question: Implementing Differential Operator applied to Matrix



I am quite new to Maple and require some help on vector calculus. I have a differential operator in matrix form C that has to be applied to a column vector B.

C = [d/dx   0    d/dy]

      [0     d/dy  d/dx]  


B = [alpha*L]




Thus I want to perform straightforward matrix multiplication of C*B to get,

[d/dx(alpha*L) + d/dy(phi*N) ]

[d/dy(beta*M) + d/dx(phi*N)]


and of course then automatically apply the product rule. I would be really grateful for any suggestions you might have. Many thanks!

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