Question

$\frac{d}{dx}(\log (secx+\tan x\left)\right)=$

• A. $\cos ecx$
• B. $secx$
• C. $\tan x$
• D. $\cos x$

Answer 1

The correct option is B

$secx$

Find the differentiation of given expression:

Given, $\frac{d}{dx}(\log (secx+\tan x\left)\right)$

Differentiate it with respect to $x$

$\begin{array}{rcl}\frac{dy}{dx}& =& \frac{1}{(secx+\tan x)}\times \frac{d}{dx}(secx+\tan x)\\ & =& \left[\frac{1}{(secx+\tan x)}\right]\times (secx\tan x+se{c}^{2}x)\\ & =& \left[\frac{1}{(secx+\tan x)}\right]\times secx(\tan x+secx)\\ & \mathbf{=}& \mathbf{}\mathit{s}\mathit{e}\mathit{c}\mathbf{}\mathit{x}\end{array}$

Hence, Option (B) is correct.