Question

$\frac{d}{dx}\left(\sec x^{\circ }\right)$ equals-

• A. $\sec x\tan x$
• B. $\sec x{}^{\circ }$ $\tan x{}^{\circ }$
• C. $\left(\frac{\pi }{180}\right)\sec x^{\circ }\tan x^{\circ }$
• D. $\left(\frac{\pi }{180}\right)\sec x\cot x$

Answer 1

Answer: (C)

$\left(\frac{\pi }{180}\right)\sec x^{\circ }\tan x^{\circ }$

Using chain rule,
$\frac{d}{dx}\left(\sec x^o\right)=\frac{d}{d{x}^o}\left(\sec x^o\right)\cdot \frac{d}{dx}{x}^o$
$=\left(\sec x^o\tan x^o\right)\cdot \frac{d}{dx}\left(\frac{\pi x}{180}\right)$

$=\left(\frac{\pi }{180}\right)\sec x^o\tan x^o$