A) \[y\cos \text{e}{{\text{c}}^{2}}x(1-\log \tan x)\]
B) \[y\,\text{cos}\text{e}{{\text{c}}^{2}}x(1+\log \tan x)\]
C) \[y\cos \text{e}{{\text{c}}^{2}}x(\log \tan x)\]
D) None of these
Correct Answer: A
Solution :
\[y={{(\tan x)}^{\cot x}}\Rightarrow \log y=\cot x\log \tan x\] Þ \[\frac{1}{y}\frac{dy}{dx}=\text{cose}{{\text{c}}^{\text{2}}}x-\log \tan x.\text{cose}{{\text{c}}^{2}}x\] Þ \[\frac{dy}{dx}=y\text{cose}{{\text{c}}^{2}}x(1-\log \tan x)\].
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