If $y^2 = p(x)$ is a polynomial of degree $3$,then $2\frac{d}{dx}\left( y^3 \frac{d^2y}{dx^2} \right)$ is equal to:

$A$ function $y = f(x)$ has a second-order derivative $f''(x) = 6(x - 1)$. If its graph passes through the point $(2, 1)$ and at that point the tangent to the graph is $y = 3x - 5$,then the function is

If $y = \frac{\alpha x + \beta}{\gamma x + \delta}$,then $2 y_1 y_3 =$

If $f(x)=\tan ^{-1}\left[\frac{\log \left(\frac{e}{x^{2}}\right)}{\log \left(e x^{2}\right)}\right]+\tan ^{-1}\left[\frac{3+2 \log x}{1-6 \log x}\right]$ then the value of $f^{\prime \prime}(x)$ is equal to

If $y = \frac{(\sin^{-1} x)^2}{2}$, then $(1-x^2) y_2 - x y_1 = $

Let $f(x) = x^{3} + x^{2}f^{\prime}(1) + 2x f^{\prime\prime}(2) + f^{\prime\prime\prime}(3)$, where $x \in R$. Then the value of $f^{\prime}(5)$ is: