Let $[x]$ denotes the greatest integer less than or equal to x and $f(x) = [\tan^2 x]$, then which of the following is true ?

If $\sqrt{y + x} + \sqrt{y - x} = c$ and $\dfrac{dy}{dx} = K - \sqrt{\dfrac{y^2}{x^2} - 1}$ , then the value of $K$ is

If $y = (x^2 + 1)^{\sin x}$ for $x > 0$ such that $\dfrac{dy}{dx} = y\left[\dfrac{2x \sin x}{g(x)} + \cos x \cdot \log[g(x)]\right]$, then the function $\dfrac{1}{g(x)}$ is...

The derivative of $f(\sin x)$ with respect to $g(\sec x)$ at $x = \dfrac{\pi}{4}$, given that $f'\left(\dfrac{1}{\sqrt{2}}\right) = 3$ and $g'(\sqrt{2}) = 1$ is.....