隐函数arctany x=ln
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y'=1/sinx*(sinx)'=cosx/sinx
两边对x求导得y+xy'=(1+y')/(x+y)y(x+y)+x(x+y)y'=1+y'y'[x(x+y)-1]=1-y(x+y)y'=[1-y(x+y)]/[x(x+y)-1]dy=[1-y(x+
两边微分cosydy=(dx+dy)/(x+y)[cosy(x+y)-1]dy=dxdy/dx=1/[cosy(x+y)-1]
复合函数f(x)=lnxg(x)=ln[ln(x)]r(x)=ln{lnln(x)]}r'(x)=[1/lnln(x)]g'(x)=[1/lnln(x)][1/ln(x)]f'(x)=[1/lnln(
表示以e为底的对数函数符号
由题意得:1+1x>01−x2≥0,即x<−1或x>0−1≤x≤1解得:x∈(0,1].故答案为:(0,1].
是不是想要这个In(xy)=Inx+InyIn(a^b)=bInaInx=y,则x=e^y(Inx)'=1/x.
y'=(y+xy')/(xy)xyy'-xy'=yy'=y/(xy-x)所以dy/dx=y'=y/(xy-x)
1.y‘=(e^(-5x^2))'tan3x+e^(-5x^2)(tan3x)'=-10xe^(-5x^2))'tan3x+3e^(-5x^2)(sec3x)^22.y'=cosx/(sinxlnsi
首先要知道(lnx)'=1/x,然后一步一步求1.f'(x)=4*[1/(6x+5lnx)]*(6+5/x),f'(4)就把x=4带入2.f'(x)=4*(1/lnx)*(1/x)(a^x)'=lna
直接两边对x求导,得1/y*(-1/y2)*dy/dx=1/xy*(y+xdy/dx)下面会了吧
>> T=1001:1999;>> a=(log(0.00000000000001)-7.8*log(10)+660000./(8.314*T))./3.6
y'=1/xx>0x
两边求导(y'x-y/x^2)/[1+(y/x)^2]=x+yy'/(x^2+y^2)^1/2整理y'x-y=(x+yy')(x^2+y^2)^1/2
y=u^(1/2)u=lnVV=lnpp=x^(1/2)
x=yln(xy),等式两端对x求导,1=dy/dx+y[1/ln(xy)][y+x(dy/dx)]=dy/dx+y/ln(xy)+xdy/dx,整理得(dy/dx)(1+x)=1-y/ln(xy),
y∈(-∞,0)因为底数和真数(你知道它们什么含义的哦?)一个是大于一,一个是大于0小于一,所以它们合起来的值是小于0的.y=lnx,e>1,0
这里用隐函数求导是因为很难将x分离出来,变成y=f(x)的形式.故先把y看成关于x的函数.(sinxy)'=cos(xy)(xy)'=cos(xy)(x'y+xy')=cos(xy)(y+xy')
y=x+lny两边求导:y'=1+y'/yy'(1-1/y)=1y'=y/(y-1)y‘’=[y'(y-1)-y*y']/(y-1)²=[y-y²/(y-1)](y-1)²
主要利用复合函数的求导:z=f(y),y=g(x),则z对x求导dz/dx=f'(y)*(dy/dx).等式左边对x求导过程:d(lny)/dx=(1/y)y',等式右边对x求导过程:d(x-y)/d