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sinxCos2x20阶导

^由积化和差公式,sinx*cos2x=1/2(sin3x-sinx).且知sinx的n阶导数为sinx,如果n=4k;cosx,如果n=4k+1;-sinx,如果n=4k+2;-cosx,如果n=4k+3.所以sinx*cos2x的n阶导数为1/2(3^n*sin3x-sinx),如果n=4k;1/2(3^n*cos3x-cosx),如果n=4k+1;1/2(-3^n*sin3x+sinx),如果n=4k+2;1/2(-3^n*cos3x+cosx),如果n=4k+3

sinxcos2x=1/2(sinxcos2x+cosxsin2x+sinxcos2x-cosxsin2x)=1/2(sin(x+2x)+sin(x-2x))=1/2(sin3x-sinx)

你好!y=sinxcos xcos2x =(1/2)sin2x.cos2x =(1/4)sin4xy' = cos4xy''=-4sin4x仅代表个人观点,不喜勿喷,谢谢.

根据公式:sinx导数是cosx,x^2导数是2x,将两个结果相乘:2sinx*cosx

y=sinxsin2xsin3x=-[cos4x-cos(-2x)]sin2x/2=(sin2xcos2x-sin2xcos4x)/2={sin4x/2-[sin6x+sin(-2x)]/2}/2=-sin2x/4+sin4x/4-sin6x/4 y'=-cos2x/2+cos4x-3cos6x/2 y''=sin2x-4sin4x+9sin6x y<3>=2cos2x-16cos4x+54cos6x y<4>=-4sin2x+64sin4x-324sin6x y

天哪,都出了什么问题?这么简单的求导,解得这么恐怖?先积化和差不就简单了吗?y = sinxcos3x = [sin4x - sin2x] y' = 2cos4x - cos2x y''= -8sin4x + 2sin2x 或者写成:y'' = 2sin2x - 8sin4x

y=cosx/cos2xy' = (-sinxcos2x+2cosxsin2x) / cos(2x) = -sinx/cos2x + 2cosxsin2x/cos(2x)y'' = (-cosxcos2x-2sinxsin2x) / cos(2x) + [(-2sinxsin2x+4cosxcos2x)cos(2x)-2cosxsin2x(-4cos

显然sin(x/2)*cos(x/2)=0.5 *2sin(x/2)*cos(x/2)而由二倍角公式可以知道,2sin(x/2)*cos(x/2)=sinx所以sin(x/2)*cos(x/2)=0.5sinx于是求导得到[sin(x/2)*cos(x/2)] '= (0.5sinx)'=0.5 *(sinx)'=0.5 *cosx

y =sinx/(cosx)^2 = tanxsecx, y' = (tanx)'secx+tanx(secx)' = [(secx)^2]secx+tanx(secxtanx) = …….

解析 y=sinxsinxcosx y'=sinx'sinxcosx+sinx(sinxcosx)'=cosxsinx+sinx(sinx'cosx+sinxcosx')=cosxsinx+sinx(cosxcosx-sinxsinx)=cosxsinx+sinxcos2x=1/2sin2x+sinxcos2x

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