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
用 dy / dx = (dy/dt)/(dx/dt)
t t
dy e sint + e cost cost+sint 1+tant tan(π/4)+tant
-- = ----------------- = --------- = ------- = ----------------- = tan(t+π/4)
dx t t cost-sint 1-tant 1-tan(π/4)tant
e cost - e sin t
x+y
(= ---)
x-y
再用一次
2 2 2
d y d dy (dy/dx)/dt sec (t+π/4) 1+tan (t+π/4)
---- = ---(--) = ---------- = ---------------- = ----------------
2 dx dx dx/dt t t t t
dx e cost - e sint e cost - e sint
2
1+(x+y/x-y)
= ------------
x-y
2 2
(x-y) + (x+y)
= ----------------
3
(x-y)
2 2
2(x + y )
= ------------
3
(x-y)
2t 2 2
2e (cos t + sin t )
= ----------------------
3t 3
-- e (cost-sint)
-t -3
= 2e (cos t-sint)
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◆ From: 61.231.99.118
※ 編輯: yueayase 來自: 61.231.99.118 (12/04 00:53)
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