Differentiation Question 3
Question: If $ y={{(\tan x)}^{\cot x}} $ , then $ \frac{dy}{dx}\backslash $ =
[AISSE 1985]
Options:
A) $ y\cos e{c^{2}}x(1-\log \tan x) $
B) $ ycose{c^{2}}x(1+\log \tan x) $
C) $ y\cos e{c^{2}}x(\log \tan x) $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ y={{(\tan x)}^{\cot x}}\Rightarrow \log y=\cot x\log \tan x $
Therefore $ \frac{1}{y}\frac{dy}{dx}=cose{c^{2}}x-\log \tan x.cose{c^{2}}x $
Therefore $ \frac{dy}{dx}=ycose{c^{2}}x(1-\log \tan x) $ .
BETA
