Question

导数题求解。。。

Answer 1

t=0
y=1

dx/dt=6t+2
e^y *y' sint+e^ycost-y'=0

dy/dt=e^ycost/(1-e^ysint)
dy/dt|t=0 = e

dy/dx=【e^ycost/(1-e^ysint)】/(6t+2)
=e^ycost/[(1-e^ysint)(6t+2)]
d(dy/dx)/dt
=[(e^y*y'cost -e^ysint)(1-e^ysint)(6t+2) -e^ycost*[(1-e^ysint)(6t+2)]']/[(1-e^ysint)(6t+2)]方
=[(e^y*y'cost -e^ysint)(1-e^ysint)(6t+2) -e^ycost*[(-e^y*y'sint-e^ycost)(6t+2)+6(1-e^ysint)]]/[(1-e^ysint)(6t+2)]方
t=0,y=1,dy/dt|t=0= e代入，得
d(dy/dx)/dt |t=0

=[e×e ×1×2 -e×【-e×2+6】]/[1×2]方
=(4e方-6e)/4
=e方 -3e/2

d²y/dx² |t=0

=(e方 -3e/2)/2
=e方/2 -3e/4
自己再验算下。

追问

这个，，没什么。。别的办法吗。

算了3遍。。我的天。。

追答

是啊，没有别的办法了。