1. If y = x 開方(2x+3) , show that dy/dx = x^2/y + y/x
2. If xy = 2x^2 +3 , prove that x^2 * (d^2y)/(dx^2) + x* dy/dx = y
3. If ax^2 + 2hxy + by^2 = 0 , prove that d^2y / dx^2 = 0
Differentiation
2008-08-24 10:23 pm
回答 (3)
2008-08-24 11:49 pm
✔ 最佳答案
As follows:圖片參考：http://hk.geocities.com/stevieg_1023/0AMATHS1.gif
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2008-08-24 11:43 pm
y = x 開方(2x+3)
y^2=(2x+3)x^2
Diff. both sides w.r.t. x
2y(dy/dx)=(2x+3)(2x)+2x^2
dy/dx=[x(2x+3)+x^2]/y
dy/dx=x^2/y+x(2x+3)/y
dy/dx=x^2/y+[sqrt(2x+3)]
∴dy/dx=x^2/y+y/x
xy = 2x^2 +3
Diff. both sides. w.r.t. x
x(dy/dx)+y=4x
dy/dx=(4x-y)/x
dy/dx=4-y/x
d^2y/dx^2=-[x(dy/dx)-y]/x^2
d^2y/dx^2=[y-x(4-y/x)]/x^2
d^2y/dx^2=(2y-4x)/x^2
∴x^2 * (d^2y)/(dx^2) + x* dy/dx
=(2y-4x)+x(4-y/x)
=y
y^2=(2x+3)x^2
Diff. both sides w.r.t. x
2y(dy/dx)=(2x+3)(2x)+2x^2
dy/dx=[x(2x+3)+x^2]/y
dy/dx=x^2/y+x(2x+3)/y
dy/dx=x^2/y+[sqrt(2x+3)]
∴dy/dx=x^2/y+y/x
xy = 2x^2 +3
Diff. both sides. w.r.t. x
x(dy/dx)+y=4x
dy/dx=(4x-y)/x
dy/dx=4-y/x
d^2y/dx^2=-[x(dy/dx)-y]/x^2
d^2y/dx^2=[y-x(4-y/x)]/x^2
d^2y/dx^2=(2y-4x)/x^2
∴x^2 * (d^2y)/(dx^2) + x* dy/dx
=(2y-4x)+x(4-y/x)
=y
2008-08-24 11:32 pm
唔知係咪咁做呢!!!!!!
As follow AS~~~~
圖片參考：http://www.photo-host.org/img/981794screenhunter_01_aug._24_15.24.gif
圖片參考：http://www.photo-host.org/img/604677screenhunter_02_aug._24_15.24.gif
As follow AS~~~~
圖片參考：http://www.photo-host.org/img/981794screenhunter_01_aug._24_15.24.gif
圖片參考：http://www.photo-host.org/img/604677screenhunter_02_aug._24_15.24.gif
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