Question

若将函数y=f(x)sinx的图像向左平移4/π个单位得到函数y=1-2sin方x的图像，则f’(x)=

Answer 1

y=1-2sin方x=cos2x,所以原函数为所的函数向右平移4/π即 f(x)=cos2(x-4/π)=cos(2x-π/2)=sin2x,所以f'(x)=2cos2x

Answer 2

y=1-2sin方x=cos2x,所以原函数y=cos2(x-4/π)=cos(2x-π/2)=sin2x=2sinxcosx,所以f(x)=2sinx