请问一下一个数学导数问题:函数y=xsin(2x-π/2)cos(2x+π/2)的导数是多少?要解题过程要解题过程.谢谢帮忙.

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请问一下一个数学导数问题:函数y=xsin(2x-π/2)cos(2x+π/2)的导数是多少?要解题过程要解题过程.谢谢帮忙.
请问一下一个数学导数问题:函数y=xsin(2x-π/2)cos(2x+π/2)的导数是多少?要解题过程
要解题过程.谢谢帮忙.

请问一下一个数学导数问题:函数y=xsin(2x-π/2)cos(2x+π/2)的导数是多少?要解题过程要解题过程.谢谢帮忙.
原函数y=xsin(2x-π/2)cos(2x+π/2)的导数为 y'=x'sin(2x-π/2)cos(2x+π/2)+x[sin(2x-π/2)]'cos(2x+π/2)+xsin(2x-π/2)[cos(2x+π/2)]' y'=sin(2x-π/2)cos(2x+π/2)+xcos(2x-π/2)(2x-π/2)'cos(2x+π/2)-xsin(2x-π/2)sin(2x+π/2)(2x+π/2)' y'=sin(2x-π/2)cos(2x+π/2)+2xcos(2x-π/2)cos(2x+π/2)-2xsin(2x-π/2)sin(2x+π/2) 由于sinx=cos(x-π/2),cosx=sin(x+π/2),sin(x-π/2)=-cosx,cos(x+π/2)=-sinx所以 y'=cos2xsin2x-2xsin2xsin2x+2xcos2xcos2x y'=1/2sin4x+2xcos4x