Question

The derivative of $\tan x-x$ with respect to $x$is

• A. $1-{\tan }^{2}x$
• B. $\tan x$
• C. $-{\tan }^{2}x$
• D. ${\tan }^{2}x$

Answer 1

The correct option is D

${\tan }^{2}x$

Explanation for the correct answer:

Option (D):

Let $y=\tan x-x$

Then $\frac{dy}{dx}=\frac{d}{dx}\left(\tan x-x\right)$

$=\frac{d}{dx}\tan x-\frac{d}{dx}x$

$=se{c}^{2}x-1$

$={\tan }^{2}x$

Hence, Option D is the correct answer.