参数方程确定的三阶导数x=1-t^2

x't=2ty't=1-1/(1+t^2)=t^2/(1+t^2)y'=dy/dx=y't/x't=t/[2(1+t^2)]d^y/dx^2=d(y')/dx=d(y')/dt/x't=1/2*[1+

symstx=log(sqrt(1+t^2));y=atan(t);%一阶导数Dyx1=diff(y,t)/diff(x,t)%二阶导数Dyx2=diff(Dyx1,t)/diff(x,t)结果:Dy

dx=-2tdtdy=(1-3t²)dt所以dy/dx=(3t²-1)/2t

dx/dt=-2tdy/dt=1-2tdy/dx=(dy/dt)/(dx/dt)=(1-2t)/(-2t)=-1/(2t)+1

x't=-3e^(-t)y't=2e^ty'=y't/x't=-2/3*e^(2t)y"=dy'/dx=d(y')/dt/x't=-4/3*e^2t/(-3e^(-t))=4/9*e^(3t)

解;dy/dt=1-2t²dx/dt=-2t∴dy/dx=t-1/2t∵x=1-t²∴t=√(1-x)∴dy/dx=√(1-x)-1/2√(1-x)

x=arcsint;y=sqrt(1-t^2)所以dy/dx=(dy/dt)/(dx/dt)=（-2t/sqrt(1-t^2)）/(1/sqrt(1-t^2))=-t=-sinx所以d^2y/dx^2

x=e^ty=ln√(1+t)dy/dt=1/[2(1+t)]dx/dt=e^t利用参数方程求导的方法dy/dx=(dy/dt)÷(dx/dt)=1/[2e^(t)*(1+t)]d²y/dx

dy/dx=y'(t)/x'(t)=(sint+tcost)/(1-cost+tsint)再问：要过程谢谢再答：dy=y'(t)dt.dx=x'(t)dt=>dy/dx=y'(t)/x'(t)

dx/dt=2dy/dt=8tdy/dx=(dy/dt)/(dx/dt)=4t=2x

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

y''=d(dy/dx)/dx=[d(dy/dx)/dt]*(dt/dx)你所说的"又乘了个1/g'(t)",其实就是(dt/dx)

书上给的公式也只有两阶导呀.

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

dx/dt=1-1/(1+t)=t/(1+t)dy/dt=3t^2+2t=t(3t+2)y'=dy/dx=(3t+2)(t+1)=3t^2+5t+2y"=dy'/dx=(dy'/dt)/(dx/dt)

dx/dt=1-1/(1+t^2)=t^2/(1+t^2)dy/dt=2t/(1+t^2)dy/dx=(dy/dt)/(dx/dt)=2t/t^2=2/t同理求d^2x/dt^2=2t/(1+t^2)

解；一阶导数：y‘=dy/dx=(3-3t²)/(2-2t)=3/2(1+t)二阶导数：y‘’=d²y/dx²=[3/2(1+t)]'/(2t-t²)'=3/2

dx=-2tdtdy=(-3t^2+1)dtdy/dx=(dy/dt)(dt/dx)=(3t^2-1)/2td^2y/dx^2=d(dy/dx)/dx=[d(dy/dx)/dt](dt/dx)=[(6

dx/dt=-2tdy/dt=1-3t^2dy/dx=(dy/dt)/(dx/dt)=(1-3t^2)/(-2t)

“由参数方程x=cost,y=sint所确定的函数y=y(x)的二阶导数”：与求(d^2y)/(dx^2)的意思是一样的.1、函数y=y(x)的一阶导数的计算：dy/dx=dy/dt/(dx/dt)=