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

If $$f(1)=1, f^{\prime}(l)=3$$, then the derivative of $$f(f(f(x)))+(f(x))^2$$ at $$x=1$$ is

If $$y=x^{\sin x}+(\sin x)^x$$, then $$\frac{d y}{d x}$$ at $$x=\frac{\pi}{2}$$ is