x=arctant,2y-ty*2-搜答案-搜搜考试网

X=arctantdx/dt=1/(1+t^2)y=ln(1+t2)dy/dt=2t/(1+t^2)dy/dx=(dy/dt)/(dx/dt)=2td2y/dx2=d(dy/dx)/dx=2dt/dx

dy/dx=(dy/dt)/(dx/dt)=[2t/(1+t^2)]/[1-1/(1+t^2)]=2/t

这是参数方程求导x'=t/（1+t^2)y'=1/（1+t^2)x''=[（1+t^2)-t*2t]/（1+t^2)^2=（1-t^2)/（1+t^2)^2y''=-2t/（1+t^2)^2dy/dx

dy/dx=(dy/dt)/(dx/dt)显然dx/dt=1/(1+t²)给出的y是关于t的隐函数,可以不管这些,直接把y看成是t的函数,然后两边求导,得2dy/dt-(y²+2t

-(t^2+1)/(4t^3)dy/dt=1/(t*t+1)dx/dt=2t/(t*t+1)dy/dx=1/2td^2y/dx^2=[d(1/2t)/dt]*(t*t+1)/2t=-(t^2+1)/(

dy/dx=[1-1/(1+t²)]/[2t/(1+t²)]=t/2d²y/dx²=(1/2)*dt/dx=(1/2)/(dx/dt)=(1/2)/[2t/(1

dx/dt=1-2t/(1+t^2)=(1+t^2-2t)/(1+t^2)=(t-1)^2/(1+t^2)dy/dt=1/（1+t^2)y'=1/(t-1)^2dy'/dt=-2/(t-1)^3y"=

f(tx,ty)=t^2[f(x,y)]

y=e^ty+xy-x=e^tyty=ln(y-x)t=ln(y-x)/y平方得t²=ln²(y-x)/y²(1+x²-y²)y²=ln&#

书上给的公式也只有两阶导呀.

答：x=ln(1+t²),x'(t)=2t/(1+t²)y=t-arctant,y'(t)=1-1/(1+t²)=t²/(1+t²)dy/dx=(dy

解答如图

先分别求出dx/dt和dy/dt,假设A=dx/dt,B=dy/dt然后用B/A得出dy/dx设C=B/A=dy/dxC中只含有t.因此,d^2y/dx^2=C/dt乘以dx/dt的倒数（dt/dx）

分别算出dx,dy,然后相除就行详见参考资料

dx/dt=2t/(1+t²)dy/dt=1/(1+t²)dy/dx=1/(2t)d(dx/dt)/dt=(2-4t²)/(1+t²)²d(dy/dt

∵dx=2tdt/√(1+t²)dy=dt/(1+t²)∴dy/dx=[2tdt/√(1+t²)]/[dt/(1+t²)]=2t√(1+t²).

点击放大,荧屏放大再放大：

应该是求的d2y/dx2吧,这个不能求d2y/d2x

x=tany+ln(cosy^2),dy/dx=(dx/dy)^-1=(tany-1)^-2,y"=d(dy/dx)/dy*dy/dx=-2secy^2/(tany-1)^5