微分問題,微分大大請近

f(v)=a/[v(v+b)+b(v-b)]

f(v)=a(v²+2bv-b²)^(-1)


f'(v)=a[d.c.of(v²+2bv-b²)^(-1)

×[d.c.of(v²+2bv-b²)]


f'(v)=a[-1(v²+2bv-b²)^(-2)](2v+2b)


f'(v)=-2a(b+v)/(v²+2bv-b²)²


f"(v)=-2a{(v²+2bv-b²)²[d.c.of(b+v)]


-(b+v)[d.c.of(v²+2bv-b²)²]}


/[(v²+2bv-b²)²]²


f"(v)=-2a{(v²+2bv-b²)²


-(b+v)[2(v²+2bv-b²)²(2v+2b)]}


/(v²+2bv-b²)⁴

f"(v)=-2a{(v²+2bv-b²)²


-(b+v)[2(v²+2bv-b²)(2v+2b)]}


/(v²+2bv-b²)⁴


f"(v)=-2a[(v²+2bv-b²)²


-4(b+v)²(v²+2bv-b²)]


/(v²+2bv-b²)⁴


f"(v)=-2a(v²+2bv-b²)[(v²+2bv-b²)-4(b+v)²]


/(v²+2bv-b²)⁴


f"(v)=-2a(v²+2bv-b²-4b²-8bv-4v²)


/(v²+2bv-b²)³


f"(v)=-2a(-5b²-6bv-3v²)/(v²+2bv-b²)³


f"(v)=2a(5b²+6bv+3v²)/(v²+2bv-b²)³

a&b是常數嗎?!
沒定義?!

2011-10-06 23:10:07 補充：
若a&b為常數
一次微分：
-a[v^2+2bv+b^2]^(-2)*(2v+2b)
二次微分：
-a*(-2)[v^2+2bv+b^2]^(-3)*(2v+2b)
=2a*[v^2+2bv+b^2]^(-3)*(2v+2b)

a b are const.
[v(v+b)+b(v-)b]^(-1)
by chain rule
一階導數
{-1*[v(v+b)+b(v-b)]^(-2)}*[2v+b+b]
二階導數
不會，好難...用微分乘法公式就解的出來了，即前微後不微+前不微後微~

對什麼微分又沒說~~