y=log(secx) হলে dy/dx=কত?

If the prime sign (') represents differentiation w.r.t. $x$ and $f^{'}=\sin x+\sin 4x.\cos x$, then $f^{'}\left ( 2x^{2}+\cfrac{\pi }{2} \right )$ at $x=\sqrt{\dfrac{\pi }{2}}$ is equal to

If $\displaystyle \frac { \cos ^{ 4 }{ \theta } }{ x } +\frac { \sin ^{ 4 }{ \theta } }{ y } =\frac { 1 }{ x+y }$ then $\displaystyle \frac { dy }{ dx } =$

For $n\epsilon N$, let $f\left ( x \right )=min\:\left \{ 1-\tan ^{n}x, 1-\sin ^{n}x, 1-x^{n} \right \}$, $x\epsilon \left ( -\cfrac {\pi}{2}, \cfrac {\pi}{2} \right )$. The left hand derivative of $f$ at $x=\cfrac {\pi}{4}$ is

The ant derivative of $\dfrac{1}{\left(1+x\tan x\right)^{2}}$ with respect to $x$ is equal to