If $y=x \log \left(\frac{x}{2-3 x}\right)$ for $0 < x < \frac{2}{3}$,then $\frac{d^2 y}{d x^2}$ at $x=\frac{1}{2}$ is

If $y = (\tan^{-1} x)^2$,then $(x^2 + 1)^2 \frac{d^2 y}{dx^2} + 2x(x^2 + 1) \frac{dy}{dx} = $

The second derivative of the function $y = f(x)$ is $f''(x) = 6(x - 1)$. If the graph of the function passes through the point $(2, 1)$ and the equation of the tangent at that point is $y = 3x - 5$,find the equation of the function.

If $\left(\frac{dy}{dx}\right) = \frac{1}{\left(\frac{dx}{dy}\right)}$ and $\frac{d^2x}{dy^2}\left(\frac{dy}{dx}\right)^3 + \frac{d^2y}{dx^2} = k$, then $e^{k f(x)} - k f(x) =$

If $y = \log(\log x)$,then $\frac{d^2y}{dx^2}$ is equal to

Find the second order derivative of the function $f(x) = x^{2} + 3x + 2$.