If $$y$$ is a function of $$x$$ and $$\log (x+y)=2 x y$$, then $$\frac{d y}{d x}$$ at $$x=0$$ is

If $$x=3 \tan \mathrm{t}$$ and $$y=3 \sec \mathrm{t}$$, then the value of $$\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$$ at $$\mathrm{t}=\frac{\pi}{4}$$ is

If $$y=\tan ^{-1}\left(\frac{\log \left(\frac{\mathrm{e}}{x^2}\right)}{\log \left(e x^2\right)}\right)+\tan ^{-1}\left(\frac{4+2 \log x}{1-8 \log x}\right)$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ is

If $$y=\cos ^{-1}\left(\frac{\mathrm{a}^2}{\sqrt{x^4+\mathrm{a}^4}}\right)$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ is