$\text{ If }{f}^1\left(1\right)=2,g^1\left(\sqrt{2}\right)=4\text{ then }\frac{d\left(f\right(\tan x\left)\right)}{d\left(g\right(\sec x\left)\right)}\text{ at }x=\frac{\pi }{4}\text{ is }$

$\frac{{\mathrm{f}}^{\mathrm{\prime }}(\tan \mathrm{x})\cdot {\sec }^2\mathrm{x}}{{\mathrm{g}}^{\mathrm{\prime }}(\sec \mathrm{x})\sec \mathrm{x}\cdot \tan \mathrm{x}}=\frac{{\mathrm{f}}^{\mathrm{\prime }}\left(1\right)(\sqrt{2}{)}^{{\gamma }^{\mathrm{\prime }}}}{{\mathrm{g}}^{\mathrm{\prime }}\left(\sqrt{2}\right)\sqrt{2}\cdot 1}=\frac{2\sqrt{2}}{4}=\frac{1}{\sqrt{2}}=0.707$