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

If `f(x)=(|x|)^(|sinx|),` then `f'(-pi//4)` is equal to

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))`

Text Solution

Verified by Experts

The correct Answer is:
D
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