x এর সাপেক্ষে $\sqrt{\sin{\sqrt x}}$ এর অন্তরক সহগ-

$\frac{d}{d x}\left(\operatorname{cosec}^{-1} x\right)$ এর মান কোনটি? [Din.B'22]

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?