air asked in 科學數學 · 1 decade ago

隱微分implicit diff.的問題~~~

For following problems ,please find dx/dy,dy/dx=? Are they reciprocal of each other?

1.x^3-y^2=6xy

2.x^2=(x+y)/(x-y)

3.cos(xy)=y

Find d^2y/dx^2for the following problems(with no dy/dx invovled)

1.3x^2-4y^2=7

2.√(xy^2)-2y=3

Update:

能不能麻煩1111大大把剩下的也都解出來??因為類似的題型其實有些我也會做..但這幾題我就是不行...謝謝!!!

還有..我發現我給的贈點有點少...對不起..我會反省的~~~

1 Answer

Rating
  • 1111
    Lv 7
    1 decade ago
    Favorite Answer

    1.x^3-y^2=6xydefine y'=dy/dx,x'=dx/dy3x^2-2yy'=6y+6xy'3x^2-2yy'=6y+6xy'y'(2y+6x)=3x^2-6yy'=dy/dx=(3x^2-6y)/(2y+6x)3x^2x'-2y=6yx'+6xx'(3x^2-6y)=6x+2yx'=dx/dy=(6x+2y)/(3x^2-2y)2.  3. 遵此要領Find d^2y/dx^2for the following problems(with no dy/dx invovled)1.3x^2-4y^2=76x-8yy'=0y'=3x/4yy''=(3*4y-4y'*3x)/y^2=(12y-12x*(3x/4y))/y^2=(12y^2-9x^2)/y^32  遵此要領

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