y+sin平方+cos3x+求导

蓝峰侦2808为什么说函数f(x)=x平方+sin平方x+cos平方x 与g(t)=1+t 平方的对应法则相同? -
耿路俊14739061559 ______ 因为sin²x+cos²x=1 所以f(x)=x²+sin²x+cos²x=x²+1 与f(t)=1+t²的对应法则是相同的.

蓝峰侦2808已知函数y=(sinx+cosx)平方+2cos平方x 求递增区间 最大值最小值 -
耿路俊14739061559 ______ y=(sinx+cosx)平方+2cos平方x =sin^2x+2sinxcosx+cos^2x+2cos^2x =1+sin2x+cos2x+1 =√2(sin2xcosπ/4+cos2xsinπ/4)+2 =√2sin(2x+π/4)+2 所以递增区间是2kπ+π/2>=2x+π/4>=2kπ-π/22kπ+π/4>=2x>=2kπ-3π/4 kπ+π/8>=x>=kπ-3π/8 最大值是√2+2 最小值是-√2+2

蓝峰侦2808函数y=sin2x+2cosx的最大值和最小值 -
耿路俊14739061559 ______ sin2x 是sin平方x 还是 sin(2x).如果是sin平方x的话那么y = sin^2 x + 2cosx = -cos^2 x + 2cosx + 1= -(cosx - 1)^2 + 2因为 cosx 属于 [-1,1]所以 cosx - 1 属于 [-2,0], (cosx...

蓝峰侦2808函数【y=cos(π/3 - x)的平方】的单调递增区间 -
耿路俊14739061559 ______ 半角公式 [cos(π/3-x)]^2=[1+cos2(π/3-x)]/2 y=cos(2π/3-2x)/2+1/2 y=cos(2x-2π/3)/2+1/2 当2x-2π/3∈(-π+2kπ,2kπ)时,单调递增 当x∈(-π/6+kπ,π/3+kπ),单调递增

蓝峰侦2808化简sinx+sin(x+2π/3)+cos(x+5π/6) -
耿路俊14739061559 ______ =sinx+sin(x+2π/3)+sin(x+4π/3)=sinx+sin(x+2π/3)+sin(x+2π/3)cos(2π/3)+sin(2π/3)cos(x+2π/3)=sinx+sin(x+2π/3)-(1/2)sin(x+2π/3)+(√3/2)cos(x+2π/3)=sinx+(1/2)sin(x+2π/3)+(√3/2)cos(x+2π/3)=sinx+sin(x+2π/3+π/3)=sinx+sin(x+π)=sinx-sinx=0

蓝峰侦2808已知sinα+sinβ+siny=0,cosα+cosβ+cosy=0,求cos(β - y)的值 -
耿路俊14739061559 ______ sinα=-sinβ-sinycosα=-cosβ-cosy两边平方相加sinα^2+cosα^2=sinβ^2+siny^2+cosβ^2+cosy^2+2sinβsiny+2cosβcosy1=1+1+2cos(β-y)2cos(β...

蓝峰侦2808函数y=sin平方x+根号3sinxcosx在区间[π/4,π/2]上的最大值 -
耿路俊14739061559 ______ 解:y=sin²x+√3sinxcosx =(1-cos2x)/2+√3/2sin2x =√3/2sin2x-1/2cos2x+1/2 =cosπ/6sin2x-sinπ/6cos2x+1...

蓝峰侦2808函数y=sin平方(2x+π/3)的导数y'=2sin(2x+π/3)*cos(2x+π/3)*2这一步是怎么求出来的 cos(2x+π/3)后面为什么乘以2 -
耿路俊14739061559 ______[答案] 看作是复合函数 y=u^2 u=sinv v=2x+π/3 分别对其求导,并相乘 所以 y'=2sin(2x+π/3)*cos(2x+π/3)*2 y'=4sin(2x+π/3)cos(2x+π/3)=2sin(4x+2π/3) 对于你问的cos(2x+π/3)后面为什么乘以2,是对V求导得2 y'=2sin(2x+π/3); u′=cos(2x+π/3):v′=2这三者相乘得 ...

蓝峰侦2808函数y=sin平方x+根号3sinxcosx+2cos平方x,求周期和值域, -
耿路俊14739061559 ______[答案] f(x)=(sinx)^2+「3sinxcosx+2(cosx)^2=(sinx)^2+(cosx)^2+(cosx)^2+「3sinxcosx=1+(1+cos2x)/2+(「3/2)*2cosxsinx=3/2+sin(2x+派/6)~~~T=2派/2=派~~~f(x)值域为[0.5,2.5]~~~~~~~~~~~~$@\$\\~~(「表根号,手机打不出根号)→→←←←相关公式:倍...

蓝峰侦2808y=sin{cos平方(x三次方+x)}的导数和y=根号下1+ln方x的导数, -
耿路俊14739061559 ______[答案] 从里向外分布求导 (1)y=sin[cos^2(x^3+x)] 令t=cos^2(x^3+x),则y=sint 导数为y'=cost*t' 同理依次求导 得出最终答案为 y'=-cos[cos^2(x^3+x)]*sin(2x^3+2x)*(3x^2+1) (2)y=√[1+(lnx)^2] 令t=1+(lnx)^2,则y=√t 导数为y'=1/(2√t)*t' 依次求导 得出最终答案...