→ doublewhi :應該是隱函數解吧..顯函數解非常難求 12/03 23:13
※ 引述《allthoe2 ( )》之銘言：
: In Exercise 1-8,find the derivative dy/dx by solving
: each of implicit equation for y explixitly in term of x and (b) by
: differentiating each of the equations implixitly .show that ,in each case
: ,the result are equivalent 題目
: 1.xy-y-1=0
(x-1)y=1
y=1/(x-1)
-1
dy/dx= ────
(x-1)^2
: 2.x^1/3+y^1/3=1
y^(1/3) =1-x^(1/3)
1 dy 1
── y^(-2/3)─── = -──x^(-2/3)
3 dx 3
: 3.(2x+3y)^1/3=x^2
d(2x+3y)
(1/3)(2x+3y)^(-2/3) ──── = 2x
dx
1 3dy
──(2x+3y)^(-2/3)(2+───) = 2x
3 dx
: 4. (2x+3y)^1/3=x^2
同Question 3
: 5.x^3/1+y^3/1=5
這題目 看不懂@@
如果你是要問 x^(1/3)+y^(1/3)=5的話
dy
(1/3)x^(-2/3)+(1/3)y^(-2/3) ─── =0
dx
dy/dx都幫你求出來了
移項做化減 就可以求出y'的顯函數解了
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※ 編輯: zi6ru04zpgji 來自: 111.243.133.149 (12/03 21:57)