Re: [微積] 微分一問
※ 引述《redwing119 (翼迷)》之銘言：
: x=e^t cost
: y=e^t sint
: 2
: d y
: 求------??
: 2
: d x
2
d y d dy
------ = ----(----)
dx^2 dx dx
d dy dt dt
= ----(---- ----)* ----
dt dt dx dx
d t t 1 dt
= ----[(e sint + e cost) * ---------------------] * ----
dt e^t * (cost - sint) dx
d cost + sint 1
= ----(-------------) * ---------------------
dt cost - sint e^t * (cost - sint)
2 2
(cost - sint) + (cost + sint) 1
= --------------------------------- * ---------------------
1 - 2costsint e^t * (cost - sint)
-t
2e
= --------------------------
(1 - sin2t)(cost - sint)
--
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