If $f : R \to R$ is an even function then

Let $t \in (0, 1)$ and $\alpha \in \left(0, \dfrac{\pi}{4}\right)$. If $x = \text{cosec}^{-1}\left(\dfrac{1+t^2}{2t}\right)$, $y = \cot^{-1}\left(\dfrac{\sqrt{1-t^2}}{t}\right)$ and $\dfrac{dy}{dx} = f(t)$, then the value of $f(\tan\alpha)$ is

If $x\,e^{xy} = y + \sin^2 x$, then the value of $\dfrac{dy}{dx}$ at $x = 0$ is equal to

If $g(x) = (x^2 + 2x + 1)\cdot f(x)$ such that $f(0) = 5$ and $\lim\limits_{x \to 0}\dfrac{f(x)-5}{x} = 4$ then $g'(0) = $