left{frac{d}{d x}left(sec x^{circ}right)right | vedclass

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Question

(C) First,convert the angle from degrees to radians: $x^{\circ} = x 	imes \frac{\pi}{180} 	ext{ radians}$.Thus,$\sec(x^{\circ}) = \sec\left(\frac{\p

Vedclass · Accepted Answer

$\frac{\pi}{270}$

Vedclass · Answer

(C) First,convert the angle from degrees to radians: $x^{\circ} = x 	imes \frac{\pi}{180} 	ext{ radians}$.Thus,$\sec(x^{\circ}) = \sec\left(\frac{\pi x}{180}ight)$.Let $f(x) = \sec\left(\frac{\pi x}{180}ight)$.Using the chain rule,the derivative is $f'(x) = \sec\left(\frac{\pi x}{180}ight) 	an\left(\frac{\pi x}{180}ight) 	imes \frac{\pi}{180}$.At $x = 30$,we have $f'(30) = \sec\left(\frac{30\pi}{180}ight) 	an\left(\frac{30\pi}{180}ight) 	imes \frac{\pi}{180}$.This simplifies to $f'(30) = \sec\left(\frac{\pi}{6}ight) 	an\left(\frac{\pi}{6}ight) 	imes \frac{\pi}{180}$.Since $\sec\left(\frac{\pi}{6}ight) = \frac{2}{\sqrt{3}}$ and $	an\left(\frac{\pi}{6}ight) = \frac{1}{\sqrt{3}}$,we get:$f'(30) = \left(\frac{2}{\sqrt{3}}ight) \left(\frac{1}{\sqrt{3}}ight) 	imes \frac{\pi}{180} = \frac{2}{3} 	imes \frac{\pi}{180} = \frac{\pi}{270}$.Therefore,the correct option is $C$.

$\left\{\frac{d}{d x}\left(\sec x^{\circ}\right)\right\}_{x=30} = $ . . . . . . .

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