Second derivate of at determint det(A(t))

I have a 1500x1500 matrix function, H(s). The matrix H(s) is symmetric
and in some neighborhood of s=0 it is also positive definite. I know
the 3 derivates H(s), H'(s) and H''(s) taken in the point s=0.

Now I would like to calculate the second derivate of the determinant,
det(H(s)) taken in the point s=0. Is there a simple way to do this
calculation?

Thanks in advance

Niels

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