函数y=cot4x由y=cot u和 复合得到
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函数y=arctane^x求dyy'=e^x/(1+e^2x)dy=e^xdx/(1+e^2x)函数y=y(x)由方程x-y-e^y=0确定,求y'(0)两边对x求导:1-y'-y'e^y=0y'=1
lny+x/y=0等式两边求导:y'*1/y+1/y+x*y'(-1/y²)=0(1/y-x/y²)y'=-1/y∴y'=(-1/y)/(1/y-x/y²)=-y/(y-
由隐函数微分法可得:-sin(x+y)(1+y′)+y′=0-sin(x+y)+[1-sin(x+y)]y′=0∴y′=sin(x+y)/[1-sin(x+y)].
两边同时对X求导y+xy`=e^x+y`y`=(e^x-y)/(x-1)
大致能看清楚吧,就是把原式转化成e^xsinydx+(e^xcosy+2y)dy=o这个全微分方程,然后用全微分方程的方法做,答案是e^xsiny+y^2=C
(1)T=π/(1/2)=2π(2)f(0)=f(-π/4)a=sin(-π/2)=-1(3)f(x)=[1+cos(x-π/2)]/2+[1-cos(x-π/2)]+1=2+(1/2)sinx-(1
y'=-2sin2(x+y)-2y'sin2(x+y)(1+2sin2(x+y))y'=-2sin2(x+y)y'=-2sin2(x+y)/(1+2sin2(x+y))
偶,cotx=x,cotx的定义域为(2kл,2kл+л),那么y=cos(arccotx)相对称的定义域内为偶函数.
2cot3(x-π/12)一个对称中心是(π/12,0)
y=cotx的定义狱为x不等于KPAI所以cosxK不等于KPAI由于-1=
y=cot(u)u=sqr(v)v=4x^5+3x-1
dy/dx=-csc²(x+y)*(x+y)'=-csc²(x+y)*(1+y')=-csc²(x+y)*-y'csc²(x+y)y'=-csc²(x
f(x+2π)=√cot[(X+2π)/2+π/3]=√cot[(X/2+π/3)+π]==√cot(X/2+π/3)=f(x)所以周期T=2π.备注:本题用的是周期函数的定义.在你们学习三角函数的周
方程y=sin(x+y)两边对x求导数有:y'=cos(x+y)(x+y)'=cos(x+y)(1+y')移项整理得:[1-cos(x+y)]y'=cos(x+y)因此:y'=cos(x+y)/[1-
y'=-e^y-xe^y*y'(1+xe^y)y'=-e^yy'=-e^y/(1+xe^y)
y'=(x)'e^y+x(e^y)'y'=e^y+xe^y*y'再问:x(e^y)'=xe^y*y'?再答:对,因为y是x的函数,根据复合函数求导法,可得
ln(x+y)=x·lny(1+y‘)/(x+y)=lny+x/y·y‘y+y·y‘=y(x+y)lny+x(x+y)·y‘y‘=【y(x+x)lny-y】/【y-x(x+y)】再问:лл����
楼上好像写错了,要细心啊两边取对数,得lny=ln【(tan2x)^cot(x/2)】=cot(x/2)ln(tan2x)两边再分别求导,得y'/y={-[csc(x/2)]^2*ln(tan2x)}
两边对x求导xy^2+sinx=e^yy^2+2xyy'+cosx=e^y*y'y'(e^y-2xy)=y^2+cosxy'=(y^2+cosx)/(e^y-2xy)