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Iff(x)=|x|^(|sinx|),thenf'((pi)/(4)) equ...

If`f(x)=|x|^(|sinx|)`,then`f'((pi)/(4))` equals

A

`((pi)/(4))^(1sqrt2).((sqrt2)/(2)log"(4)/(pi)-(2sqrt2)/(pi))`

B

`((pi)/(4))^(1sqrt2).((sqrt2)/(2)log"(4)/(pi)+(2sqrt2)/(pi))`

C

`((pi)/(4))^(1sqrt2).((sqrt2)/(2)log"(4)/(pi)-(2sqrt2)/(pi))`

D

`((pi)/(4))^(1sqrt2).((sqrt2)/(2)log"(4)/(pi)+(2sqrt2)/(pi))`

Text Solution

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A
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