A matrix containing differential operators acting on a matrix containing functions

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Suppose I have a 2x2 operator matrix, D. Some of its elements are of the form (d/dx), and (d2/dx2). Now when this matrix is multiplied with another matrix, f, whose elements are functions of x, I will get the final matrix whose corresponding elements are differentiated.

for example: D = matrix([[d/dx, d3/dx3], [d2/dx2, d2/dx2]]) is an operator matrix which operates on a function matrix, f(x) = matrix([[x, x^2], [x^3, x]]) as D(f(x)) = D*f(x), (simple matrix multiplication).

Writing D = matrix([[diff( , x), diff( , x, 3)], [diff( , x, 2), diff( , x, 2)]]) does not work as diff() function needs an input function.

So how can I write the D() operator matrix?

PS: I could use f.apply_map(lambda e: diff(e, x)), but then it applies d/dx to all elements in f(x). Whereas, I have 'diff()' operators of different orders in the D matrix.