Question

请问一下一个数学导数问题:函数y=xsin(2x－π/2)cos(2x+π/2)...

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.

Answer 1

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