hlcyjbcgsyzxg2019-07-10TA获得超过1.1万个赞关注x=3t^2+2t+3方程两边对t求导dx/dt=6t+2e^ysint-y+1=0方程两边对t求导e^y*(dy/dt*sint+cost)-dy/dt=0整理得dy/dt=e^y*cost/(1-e^y*sint)=e^y*cost/(2-y)所以根据参数方程的求导公式dy/dx=(dy/dt)/(dx/dt)=e^y*cost/[(6t+2)(2-y)]用对数求导法先求对数ln(dy/dx)=y+lncost-ln(6t+2)-ln(2-y)对t求导d(dy/dx)/dt/(dy/dx)=dy/dt-tant-6/(6t+2)+（dy/dt)/(2-y)代入**t=0e^ysint-y+1=0可得y=1dx/dt=6t+2=2dy/dt=e^y*cost/(2-y)=edy/dx=e^y*cost/[(6t+2)(2-y)]=e/2d(dy/dx)/dt=(dy/dx)[dy/dt-tant-6/(6t+2)+（dy/dt)/(2-y)]=e(2e-3)/2所以d2y/dx2=d(dy/dx)/dt/dx/dt=e(2e-3)/4