|sin(x+π/2)|-|sinx|求导过程?

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|sin(x+π/2)|-|sinx|求导过程?

|sin(x+π/2)|-|sinx|求导过程?
|sin(x+π/2)|-|sinx|求导过程?

|sin(x+π/2)|-|sinx|求导过程?
(1)当x∈(0,π/2)时:
y=|sin(x+π/2)|-|sinx|
=sin(x+π/2)-sinx
y′=cos(x+π/2)-cosx
(2)当x∈(π/2,π)时:
y=-sin(x+π/2)-sinx
y′=-cos(x+π/2)-cosx,
(3)当x∈(π,3π/2)时,
y=-sin(x+π/2)+sinx
y′=-cos(x+π/2)+cosx.
(4)当x∈(3π/2,2π)时:
y=sin(x+π/2)+sinx
y′=cos(x+π/2)+cosx.
(5)当x在坐标轴时,y′=0.