If $$f(x)$$ and $$g(x)$$ are two functions with $$g(x)=x-\frac{1}{x}$$ and $$f \circ g(x)=x^3-\frac{1}{x^3}$$, then $$f^{\prime}(x)$$ is equals to

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

If $$x=e^\theta \sin \theta, y=e^\theta \cos \theta$$ where $$\theta$$ is a parameter, then $$\frac{d y}{d x}$$ at $$(1,1)$$ is equal to

If $$y=e^{\sqrt{x \sqrt{x} \sqrt{x}}...,} x >1$$, then $$\frac{d^2 y}{d x^2}$$ at $$x=\log _e 3$$ is