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diff only works on symbolic expression (elements of the symbolic ring SR), not on python objects like functions. But you are in luck because f(*v) is precisely an element of SR. So the correct syntax is f(*v).diff(v[i]).

As a side remark, f can be simplified a lot, by defining f = (M*vector(v)).norm(). In this case, f is a symbolic expression.

Here is a code that computes all the partial derivatives for some matrix M:

n = 3
v = list(var('v_%d' % i) for i in range(1, n+1))

M = Matrix([[1, 0, 0],
            [0, 1, 0],
            [0, 0, 1]])

f = (M*vector(v)).norm()

[diff(f, vi) for vi in v]

The output is:

[1/2*(v_1 + conjugate(v_1))/sqrt(abs(v_1)^2 + abs(v_2)^2 + abs(v_3)^2),
 1/2*(v_2 + conjugate(v_2))/sqrt(abs(v_1)^2 + abs(v_2)^2 + abs(v_3)^2),
 1/2*(v_3 + conjugate(v_3))/sqrt(abs(v_1)^2 + abs(v_2)^2 + abs(v_3)^2)]

Of course you can take the dot product of this list with any tangent vector.