If the functions $\displaystyle f\left ( x \right )=\sin \left ( x+a \right )$ and $\displaystyle g\left ( x \right )=b\sin x+c\cos x$ satisfy $\displaystyle f\left ( 0 \right )=g\left ( 0 \right )$ and $\displaystyle {f}'\left ( 0 \right )={g}'\left ( 0 \right )$ then

$\displaystyle\frac{dy}{dx}$ at $\displaystyle t=\frac{\pi}{4}$ for $\displaystyle x=a\left[\cos{t}+\frac{1}{2}\log{\tan^2{\frac{t}{2}}}\right]$ and $y=a\sin{t}$ is

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

  $y = \sin{\left ( \frac{1}{x} \right )}$   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? 

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