求由参数方程x=3t^2+2t+3,e^ysint-y+1=0所确定的函数y=f(x)的微分dy_数学解答

求由参数方程x=3t^2+2t+3,e^ysint-y+1=0所确定的函数y=f(x)的微分dy

人气：281 ℃　时间：2019-08-21 17:45:12

解答

e^ysint-y+1=0
两边对t求导
y'e^ysint+e^ycost-y'=0
dy/dt=e^ycost/(1-e^ysint)
x=3t^2+2t+3
dx/dt=6t+2
(dy/dt)/(dx/dt)=dy/dx
=(e^ycost)/[(6t+2)(1-e^ysint)]