Differentiation Question 214
Question: If $ y=\frac{\tan x+\cot x}{\tan x-\cot x}, $ then $ \frac{dy}{dx}= $
Options:
A) $ 2\tan 2x\sec 2x $
B) $ \tan 2x\sec 2x $
C) $ -\tan 2x\sec 2x $
D) $ -2\tan 2x\sec 2x $
Show Answer
Answer:
Correct Answer: D
Solution:
$ y=\frac{\tan x+\cot x}{\tan x-\cot x}=-\frac{1+{{\tan }^{2}}x}{1-{{\tan }^{2}}x}=-\sec 2x $
$ \Rightarrow \frac{dy}{dx}=-2\sec 2x\tan 2x $ .
BETA
