[Ezra Halleck]

2. 3.5: and are two differentiable functions satisfying and . Which of the following formulas represents ?
A) B) etc

[V. Panov]

I can’t decide between A or D
For A if you actually use f(0)=0 and g(0)=1
the derivative (f/g)”(0) will always end up as 0/1 which is 0, even if you take the third, fourth, fifth derivative etc.

For D the formula makes sense to me as well.

I’m still leaning more towards A, not sure though.

[Jenny P.]

I think its A cause no matter how many times you take the derivative it still should be 0..

[Devindra]

The way I did it I got E as my answer.

(F/G)”(0) (f’g-g’f / g^2)
U=F’g-g’F
U’=F”g + g’f’ – g”f – g’f’
= f”g- g”f

U’-v-v’u / v^2

(f”g-g”f)g^2 – (2gg’)(f’g-g’f) / g^4

f”(0)-2f'(0)g'(0)

[Ezra Halleck]

The important thing to remember for this problem is that you can’t evaluate at 0 until you have finished taking the 2nd derivative. Devindra’s solution is more or less correct (actually more than less).
1. He interchanges upper case and lower, probably because MS Word autochanges the first letter to upper case when you start a sentence.
2. U’-v-v’u / v^2 should be u’v-v’u / v^2
3. He fails to mention that v=g^2.

[H Pardon]

OK so the first derivative is
(g)(f’)-(f)(g’)/g^2

[Dom]

You forgot the 2, I agree with Dev on this one

[Dom]

I hope this helps a little

[B Amarsingh]

that actually helped me out, thx. and i ended up getting the correct answer