Computing the second order Frechet derivative of P(I-XP)^(-1)

Hi, I am new to the forum. I work on control engineering and want to calculate the second order Frechet derivative of f(X)=P(I-XP)^(-1) with respect to X, X and P being positive semidefinite matrices. I tried to compute the first order one, which is -P(I-XP)^(-1)K(I-XP)^(-1), but have no idea on how to calculate the second order one... Thanks for help.

Re: Computing the second order Frechet derivative of P(I-XP)^(-1)

Remember that

so the function can be written as

Its Frechet derivative easily now equals

(also there's a minus in your formula that I can't relate to anything).

So, for the second derivative, differentiate