Question

If $y=f\left(x\right)=-cosecx\cdot cosx$, then ${\left(\frac{dy}{dx}\right)}_{x=\frac{\pi }{2}}$ is equal to

• A. $0$
• B. $\frac{1}{2}$
• C. $1$
• D. $3$

Answer 1

Answer: (C)

We have, $y=-cosecxcosx$
$\Rightarrow y=-\frac{cosx}{sinx}=-cotx$
$\therefore \frac{dy}{dx}=-\left(-cose{c}^{2}x\right)=cose{c}^{2}x$
$\therefore \frac{dy}{dx}{|}_{atx=\frac{\pi }{2}}$$={\left(cosec\frac{\pi }{2}\right)}^2={\left(1\right)}^2=1$