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You can take the derivative of a matrix and substitute x=x0 using apply_map

ev1=M0.eigenvalues

ev2=(M0.apply_map(lambda y:y.diff(x).subs(x==x0))).eigenvalues()

This takes the derivatives of all the components of M0, substitutes x=x0 and then calculates the eigenvalues of the resulting matrix.

You can take the derivative of a matrix and substitute x=x0 using apply_map

ev1=M0.eigenvalues
ev1=M0.eigenvalues()

ev2=(M0.apply_map(lambda y:y.diff(x).subs(x==x0))).eigenvalues()

This takes the derivatives of all the components of M0, substitutes x=x0 and then calculates the eigenvalues of the resulting matrix.