分类：教育/科学-理工学科-数学
问题：求导已知x=te^2t,e^t+e^y=2,求d^2y/dx^2 
已知x=te^2t,e^t+e^y=2,求d^2y/dx^2|t=0
回答：解：x'(t)=(1+2t)e^(2t),x'(0)=1,x''(t)=(3+2t)e^(2t),x''(0)=3.
e^t+e^y=2两边对t求导,得e^t+e^y(dy/dt)=0,又t=0时,x=0,y=0,故t=0时，dy/dt=-1.
又e^t+e^y(dy/dt)^2+e^y(d^2y/dt^2)=0,将t=0代入，得1+1+d^2y/dt^2=0，故
d^2y/dt^2|(t=0)=-2.从而
d^2y/dx^2||(t=0)=[1×(-2)-3×(-1)]/1^3=1.