已知f(x)=cos(x/2)[sin(x/2)-cos(x/2)],其导为?

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已知f(x)=cos(x/2)[sin(x/2)-cos(x/2)],其导为?已知f(x)=cos(x/2)[sin(x/2)-cos(x/2)],其导为?已知f(x)=cos(x/2)[sin(x/

已知f(x)=cos(x/2)[sin(x/2)-cos(x/2)],其导为?
已知f(x)=cos(x/2)[sin(x/2)-cos(x/2)],其导为?

已知f(x)=cos(x/2)[sin(x/2)-cos(x/2)],其导为?
f'(x)=-1/2*sin(x/2)*[sin(x/2)-cos(x/2)]+cos(x/2)[1/2cos(x/2)+1/2sin(x/2)]
=-1/2*sin²(x/2)+1/2sin(x/2)cos(x/2)+1/2cos²(x/2)+1/2sin(x/2)cos(x/2)
=1/2[cos²(x/2)-sin²(x/2)]+sin(x/2)cos(x/2)
=1/2cosx+1/2sinx
=√2/2sin(x+π/4)