If $f\left(x\right)=\cos x\cdot \cos 2x\cdot \cos 4x\cdot \cos 8x\cdot \cos 16x$ then $f^{\text{'}}(\pi /4)=$______

$\cos A\cos 2A\cos 2^{2}A\dots \cos 2^{n-1}A=\frac{\sin \left(2^{n}A\right)}{2^n\sin A}$

$\therefore \cos x\cos 2x\cos 4x\cos 8x\cos 16x=\frac{\sin 32x}{32\sin x}$

$f\left(x\right)=\frac{\sin 32x}{2^5\sin x}$

$\Rightarrow f\text{'}\left(x\right)=\frac{1}{32}\frac{32\cos 32x\cdot \sin x-\cos x\cdot \sin 32x}{{\sin }^{2}x}$

$\therefore f\text{'}(\pi /4)=\sqrt{2}=1.414$