First slide

Derivatives

Question

$If y = |\cos x| + |\sin x|, then \frac{dy}{dx} at x = \frac{2 π}{3} is$

Moderate

A

$\frac{1 - \sqrt{3}}{2}$
B

0
C

$\frac{1}{2} (\sqrt{3} - 1)$
D

none of these

Solution

$\begin{array}{l} In neighborhood of x = \frac{2 π}{3}, |cosx| = - \cos x and |\sin x| = \sin x \\ or y = - cosx + sinx \\ ∴ \frac{dy}{dx} = \sin x + \cos x \\ Thus, at x = \frac{2 π}{3}, we get \frac{dy}{dx} = \sin \frac{2 π}{3} + \cos \frac{2 π}{3} = \frac{\sqrt{3} - 1}{2} . \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App