Question

$\frac{d}{dx}\sec x=$

• A. $\sec x\tan x$
• B. $\cos x\tan x$
• C. $\sin x\tan x$
• D. $\sec x\cot x$

Answer 1

The correct option is A $\sec x\tan x$

$y=\sec x$
$\therefore \frac{dy}{dx}=\underset{\delta x\to 0}{lim}\frac{\sec (x+\delta x)-\sec x}{\delta x}$ ....(Change to cos)

$=\underset{\delta x\to 0}{lim}\frac{\cos x-\cos (x+\delta x)}{\delta x.\cos (x+\delta x)\cos x}$

We have used $\cos C-\cos D$, formula

$=\sin x.\frac{1}{\cos x\cos x}=\sec x\tan x$