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

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))`

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The correct Answer is:

A

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