作者LuisSantos (^______^)
看板trans_math
标题Re: [微分]
时间Wed Jan 24 00:29:11 2007
※ 引述《king911015 (早已放弃爱上你)》之铭言：
: Given x= t+e^t, y=t+t^2, find the value of d^2y/dx^2 when t=0.
dy dy/dt
---- = --------
dx dx/dt
1 + 2t
= ----------
1 + e^t
2
d y dy/dx
----- = -------
2 dx
dx
(dy/dx)/dt
= ------------
dx/dt
((2)(1 + e^t) - (e^t)(1 + 2t))/((1 + e^t)^2)
= -----------------------------------------------
1 + e^t
(2)(1 + e^t) - (e^t)(1 + 2t)
= -----------------------------
(1 + e^t)^3
2 + (2)(e^t) - e^t - (2)(t)(e^t)
= -----------------------------------
(1 + e^t)^3
2 + e^t - (2t)(e^t)
= ---------------------
(1 + e^t)^3
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