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## #1 2005-08-29 21:04:15

KiWoonG
Guest

### Differentiating

Hi everyone
I am very confused  in differentiating in fractions

x^2
f(x) =  _______
1+x^2

i know how to differentiate the numerator but not denominator
how do you differentiate the bottom???

*** i already know that   u'v-v'u     formula and i dont mean by that..
---------
v^2
i wanna know how to differentiate separately, numerator and denominator

Thank you

## #2 2005-08-29 23:38:56

ganesh
Registered: 2005-06-28
Posts: 25,083

### Re: Differentiating

f(x) = x²/(1+x²)
f(x) = x²(1+x²)-¹
Now, use the uv method:- u'v + uv'
f'(x) = 2x(1+x²)-¹ + x²(-1)(1+x²)-²(2x)

This is because you didn't want to use u/v = (u'v - uv')/v²

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #3 2005-08-30 11:50:53

kylekatarn
Member
Registered: 2005-07-24
Posts: 445

### Re: Differentiating

I don't know why you are avoiding the formula....
Anyway, just for fun, you can differentiate f(x) using my loooong method

(in pratical problems use Ganesh's method.)

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## #4 2005-08-30 13:59:00

Flowers4Carlos
Member
Registered: 2005-08-25
Posts: 106

### Re: Differentiating

i would not wanna try it ur way kylekatarn

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