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

If $$y=e^{x^2+e^{x^2+e^{x^2+\cdots \infty}}}$$, then $$\frac{d y}{d x}$$ is equal to

$$\frac{d}{d x}\left[\tan ^{-1}\left(\frac{\cos x}{1+\sin x}\right)\right]$$ is equal to

If $$x^2+y^2=1$$, then