Rotational kinetic energy and derivative by velocity

I have some object with tensor of inertia $ I_{p_{3×3}}$ and angular velocty vector $ \omega$ .

Object’s kinetic energy find as:

$ T_p=\frac{1}{2} \omega^T I_{p} \omega$

I wand find derivative by $ \omega$ .

Is the result I am getting with this code correct?

Clear["Derivative"];  ClearAll["Global`*"];  Tp = 1/2 Transpose[\[CapitalOmega]].Ip.\[CapitalOmega];  D[Tp, \[CapitalOmega]]; 

EDIT:

Is that result correct ?

$ \frac{d}{d\omega}\frac{1}{2} \omega^T I_{p} \omega=\frac{1}{2}\omega^T(I_{p}+I_{p}^T)$