$y = \sin{\left ( \frac{1}{x} \right )}$   হলে $\frac{dy}{dx}$ এর মান-

1.   $\cos{\left ( \frac{1}{x} \right )}$  
2.   $- \frac{1}{x^{2}} \cos{\left ( \frac{1}{x} \right )}$  
3. অনির্ণেয়, যখন x=0

নিচের কোনটি সঠিক? 

$y=\ln (\cos x)$ হলে, $\frac{d y}{d x}$ এর মান 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