作业帮求y=sin^2XCOS2X的导数
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/21 18:00:50
y=(cosx+2)/(sinx-1)ysinx-y=cosx+2ysinx-cosx=y+2√(y²+1)sin(x-t)=y+2,t=arctan(1/y)sin(x-t)=(y+2)/
y1=xsin2x,y2=xcos2x,y3=(x+2)e^x=>y1-y2,y3-y2分别是其对应齐次方程的解,y1-y2=x(sin2x-cos2x),y3-y2=(x+2)e^x-xcos2x其
y=sin²2xy′=2×(cos2x)×2sin2x=4cos2x·sin2x=2sin4xy〃=2(4x)′cos4x=8cos4x
第一个y'=2sinXcosxcos2x-sin^2x*2sin2x第二个y'=[1/2*sec^2x/2*]/(tanx/2)第三个y'=看不懂第四个y'=(1+(x/根号(x^2-a^2)))/(
y=sin^2x+sinx=(sin^2x+sinx+1/4)-1/4=(sinx+1/2)^2-1/4sinx=-1/2时有最小值-1/4sinx=1时有最大值2
y=sin^2x的周期为π.根据平方正弦公式,y=sin²x=(1/2)(1-cos2x）∵函数cos2x的最小正周期为T=2π/2=π,∴y=sin²x的周期也为T=π
y=sin²x=(1-cos2x)/2∴T=2π/2=π
y=sin^x+2sinxcosx=1/2-cos2x/2+sin2x=根号下(5/4)*[2sin2x/根号5-cos2x/根号5]+1/2设cosa=2/根号5,sina=-1/根号5上式=根号下
y'sin(y/x)-y/x*sin(y/x)+1=0令y/x=u,则y'=u+xu'所以(u+xu')sinu-usinu+1=0xu'sinu+1=0-sinudu=dx/x两边积分：cosu=l
1、y'=(xcos2x)'=x'cos2x+x*cos2x'=cos2x-x*sin2x*2=cos2x-2xsin2x2、limx(e^x-1)/(cosx-1)=limx(1+x+x^2/x+x
2*cos(x^2)*x/sin(x)^2-2*sin(x^2)*cos(x)/sin(x)^3
sin^2x+cos^2y=1/2∴sin^2x=1/2-cos^2y3sin^2x+sin^2y=3（1/2-cos^2y）+sin^2y=1.5-3cos^2y）+sin^2y又有sin^2y+c
y=sin(x+π/3)sin(x+π/2)=sin(x+π/3)cosx=(sinxcosπ/3+cosxsinπ/3)cosx=1/2sinxcosx+√3/2cos^2(x)[cos^2(x)指
sin^2(2x)cos2x=（1/2）(sin2x)(sin4x)=积化和差公式sinxsiny=-1/2[cos(x+y)-cos(x-y)]（1/2）(sin2x)(sin4x)=1/4(cos
∵y=cos2x在[0，2π]上有4个零点分别为π4，3π4，5π4，7π4函数y=x的零点有0∴函数f（x）=xcos2x在区间[0，2π]上有5个零点．分别为0，π4，3π4，5π4，7π4故选D
y'=2e^2xcos(e^2x)把y看成复合函数sint,t=e^m,m=2x.复合函数求导,等于三个分别求导的积
sin(x/2)的周期是4pi,cos2x的周期是pi,sin(x/2)+cos2x的周期是其最小公倍数,自然是4pi
2派比n