求y=sin(-3x 兀 4)的递增区间及对称轴

函数f（x)=sin(3x+y)是偶函数,则f(-x)=sin(-3x+y)=f(x)=sin(3x+y)由正弦函数的性质sin(π-x)=sinx及周期性可得(-3x+y)+(3x+y)=π+2kπ

tanx+tany=3(tanx)(tany)=-3tan(x+y)=(tanx+tany)/(1-tanxtany)=3/4[sin(x+y)]^2+[cos(x+y)]^2=1[sin(x+y)]

y＝sin³x-sin3x→y'＝3sinx·(sinx)'-cos3x·(3x)'→y'＝3sin²xcosx-3cosx→y'＝3(1-cos²x)cosx-3cos

2kπ-（π/2）

复合函数应该用链式法则求导：若y=g(u),u=f(x),则dy/dx=dy/du*du/dxy=sin^5xdy/dx=dsin^5x/dsinx*dsinx/dx=5sin⁴xcosx

我说说方法,你自己算右边化为SIN平方X=1/2-1/2COS2X先解方程Y”+Y=1/2得Y=1/2再解方程Y”+Y=1/2COS2X方法是令Y=C1（X）*SIN2X+C2（X）*COS2X代入方

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

y'=(cos²x)'-(sin3^x)'=2cosx·(cosx)'-cos3^x·(3^x)'=2cosx·(-sinx)-cos3^x·(3^x·ln3)=-sin2x-ln3·cos

y=sin⁴3xcos³4xdy/dx=cos³4x*d(sin⁴3x)/dx+sin⁴3x*d(cos³4x)/dx=cos

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

cos(x+y)cosy+sin(x+y)siny=cos((x+y)-y)=cosx=4/5sinx=正负3/5tanx=正负3/4

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

y=(lnx)^3+(sinx)^2y'=dy/dx=3(lnx)^2/x+2sinxcosx=3(lnx)^2/x+sin2xdy=[3(lnx)^2/x+sin2x]dx

分析：要利用正弦本身的单调性；但是,x系数符号正直接用正弦单调性；x系数为负则相反单调性；①y=2sin(-x)=-2sinx所以单调增区间为：π/2+2kπ≤x≤3π/2+2kπ,k∈Z②y=3si

2x+兀/4=[兀/2+2k兀,3兀/2+2k兀]2x=[兀/4+2k兀,5兀/4+2k兀]x=[兀/8+k兀,5兀/8+k兀]

周期就是y(x+T)=y(x),1、y(x+T)=3sin[2(x+T)+pi/4]=y(x)=3sin(2x+pi/4),2T=2pi,T=piy=1/2sin(1/2x+pi/3),2、1/2si

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

y=sin(-3x)=-sin3x单调递增区间是2kPai+Pai/2

y=sinx增区间[2kπ-π/2,2kπ+π/2]所以本题,2kπ-π/2≤π/4+2x≤2kπ+π/2kπ-3π/8