解:
分析,你的思路没有错!
x=3t+2t+3方程两边对t求导
dx/dt = 6t+2
(e^y)sint-y+1=0方程两边对t求导
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)
代入数据t=0
e^ysint-y+1=0可得y=1
dx/dt = 6t+2 = 2
dy/dt=e^y * cost / (2 - y) = e
dy/dx = e^y * cost / [(6t+2)(2-y)]=e/2
d(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
追问谢谢哥
为什么dy/dt等于那个
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/1f178a82b9014a9016836f67a1773912b21beeaf?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
不应该复合求导吗?