Question

If $y = \sec\, x^°$, then $\frac{dy}{dx}$ is equal to:

• A. $\sec\, x\, \tan \,x$
• B. $\sec \,x^°\, \tan \,x^°$
• C. $\frac{\pi}{180} \sec \,x^\circ \, \tan \, x^\circ$
• D. none of these

Answer 1

Answer: (C)

Let $y = \sec\, x°$
Now ,$x^\circ = \frac{\pi}{180} . x \:\:\: \therefore \: y =\sec \frac{\pi}{180} x$
Now, $\frac{dy}{dx} = \frac{\pi}{180} \sec \frac{x \pi}{180} \tan \frac{\pi}{180} x$
$\Rightarrow \:\: \frac{dy}{dx} =\frac{\pi}{180} \: \sec \, x^\circ . \tan \, x^\circ$