$$\begin{aligned} & \mathrm{f}(x)=(\cos x+\mathrm{i} \sin x) \cdot(\cos 3 x+\mathrm{i} \sin 3 x) \cdots {[\cos (2 \mathrm{n}-1) x+\mathrm{i} \sin (2 \mathrm{n}-1) x] \mathrm{n} \in \mathbb{N}} \end{aligned}$$

Then $\mathrm{f}^{\prime \prime}(x)=$ _______ , (Where $\mathrm{i}=\sqrt{-1}$ )

The modulus of the square root of the conjugate of $-7+24 \sqrt{-1}$ is __________