The derivative of $$\mathrm{f}(\sec x)$$ with respect to $$g(\tan x)$$ at $$x=\frac{\pi}{4}$$, where $$f^{\prime}(\sqrt{2})=4$$ and $$g^{\prime}(1)=2$$, is

If $$y=\log \sqrt{\frac{1+\sin x}{1-\sin x}}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=\frac{\pi}{3}$$ is

If $$y=\sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right)$$ then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ is equal to

If $$y^{\frac{1}{m}}+y^{\frac{-1}{m}}=2 x, x \neq 1$$, then $$\left(x^2-1\right)\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^2$$ is equal to