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

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

A

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

B

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

C

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

D

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

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The correct Answer is:

D

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