A) -1
B) 1
C) \[log\text{ }2\]
D) \[\text{ }log2\]
Correct Answer: A
Solution :
When \[x=1,\text{ }y=\frac{\pi }{2}\] \[{{({{x}^{x}}cot\text{ }y)}^{2}}=cose{{c}^{2}}y\] \[{{x}^{x}}=cot\text{ }y+|cosec\text{ }y|\] when \[x=1,y=\frac{\pi }{2}\] \[\Rightarrow \]\[{{x}^{x}}=cot\text{ }y+cosec\text{ }y\] diff. w.r.t. to\[x\] \[{{x}^{x}}(1+lnx)=(cose{{c}^{2}}ycosecy\text{ }cot\text{ }y)\frac{dy}{dx}\] when\[x=1\]and\[y=\frac{\pi }{2}\] \[\frac{dy}{dx}=-1\]
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