If f(x)=xg(x)f(x) = x^{g(x)}f(x)=xg(x) where g(x)=sin(x)g(x) = \sin(x)g(x)=sin(x), what is f′(π/2)f'(\pi/2)f′(π/2)?
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(π/2)ln(π/2)(\pi/2) \ln(\pi/2)(π/2)ln(π/2)
π/2\pi/2π/2