If $$y=x+\frac{1}{x}$$, then which among the following holds?

If $$y=\tan ^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right)$$, where $$x^2 \leq 1$$. Then, find $$\frac{d y}{d x}$$ is equal to

If $$3 \sin x y+4 \cos x y=5$$, then $$\frac{d y}{d x}$$ is equal to

$$f(x)=\sqrt{x^2+1}: g(x)=\frac{x+1}{x^2+1}: h(x)=2 x-3$$, then the value of $$f^{\prime}\left[h^{\prime}\left(g^{\prime}(x)\right)\right]$$ is equal to