求导数dy/dx（参数方程求导）x＝3t^2+2te^ysint-y+1＝0求导数dy/dx（参数方程求导）x＝3t^2+2te^ysint-y+1＝0

Question

求导数dy/dx （参数方程求导） x＝3t^2+2t e^ysint-y+1＝0
求导数dy/dx （参数方程求导）
x＝3t^2+2t e^ysint-y+1＝0

Answer 1

dx/dt=6t+2
d(e^ysint-y+1)=0,得：dy/dt*e^y sint+e^ycost-dy/dt=0,得：dy/dt=e^ycost/(1-e^ysint)
所以dy/dx=(dy/dt)/(dx/dt)=e^ycost(1-e^ysint)/(6t+2)