If $y = \cos^{-1}(\sin x)$, where $\dfrac{\pi}{2} < x < \pi$, then $\dfrac{dy}{dx} = ...$

If $y = \left(\dfrac{ax+b}{cx+d}\right)$, then $2\dfrac{dy}{dx} \cdot \dfrac{d^3 y}{dx^3}$ is equal to

Let $f(x) = 3x^3 + 4e^{\frac{x}{2}}$ and $g(x) = f^{-1}(x)$. Then the value of $g'(4)$ is equal to...

If the function $f(x) = ax^3 - bx^2 - 8x - 4$ satisfies Roll's theorem in $[1,3]$, if $f'(2) = 0$ then $a - b$ is equal to...