The differential equation obtained from the function $$y=a(x-a)^2$$ is

In a quadrilateral $$ABCD, M$$ and $$N$$ are the mid-points of the sides $$A B$$ and $$C D$$ respectively. If $$\mathbf{A D}+\mathbf{B C}=t \mathbf{M N}$$, then $$t=$$

If $$f(x)=\log (\sec x+\tan x)$$, then $$f^{\prime}\left(\frac{\pi}{4}\right)=$$

If $$f(x)=\frac{2 x+3}{3 x-2}, x \neq \frac{2}{3}$$, then the function $$f$$ of is