http://img718.imageshack.us/img718/9397/derive.png

Where did I go wrong?

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- May 1st 2010, 08:27 AMkmjtDid I derive this right?
http://img718.imageshack.us/img718/9397/derive.png

Where did I go wrong? - May 1st 2010, 08:44 AMCaptainBlack
- May 1st 2010, 08:57 AMkmjt
For somee reason I thought you can bring the denominator up and attach it, I guess you can't (Headbang)

- May 1st 2010, 09:17 AMTekken
well you can if you raise the denominators to the power of -1

i.e. $\displaystyle A = x^{2}.4\pi^{-1} + (x^{2} - 80x + 1600).16^{-1} $ but thats not reall that useful for what you want to do.

Just use the quotient rule twice and sum the two answes to get $\displaystyle A' $

Cant see how this is university level though... - May 1st 2010, 09:24 AMharish21
- May 1st 2010, 09:34 AMkmjt
So far I used the quotient rule on x^2/4pi and got 8pi x / 4pi^2, is that correct?

- May 1st 2010, 09:42 AMTekken
- May 1st 2010, 09:42 AMharish21
- May 1st 2010, 09:53 AMkmjt
I think I should stick to differentiating the left and than the right, because that's what we do in class. Heres where I got my answer from doing the quotient rule on x^2 / 4pi:

f'(x) = g'(x)h(x) - g(x)h'(x) / (4pi)^2

= (2x)(4pi) - (x^2)(0) / 4pi^2

= 8pix - 0 / 4pi^2

= 8pix / 4pi^2

Where did I mess up? I used a derivative calculator online and it said the derivative would be x / 2pi

Sorry again harish thanks for that technique but I don't believe I should be doing it that way in the class im in (Happy) - May 1st 2010, 10:06 AMTekken
Ok here goes...

let $\displaystyle u = x^{2} $ and $\displaystyle v = 4\pi $

differentiating u w.r.t x we get $\displaystyle \frac{du}{dx} = 2x $ and

differentiating v w.r.t x we get $\displaystyle \frac{dv}{dx} = 0 $ This is always the case when differentiating constants.

Applying the quotient rule we get;

$\displaystyle \frac{dy}{dx} = \frac{4\pi.2x - x^{2}.0}{4\pi^{2}} $

=> $\displaystyle \frac{dy}{dx} = \frac{8\pi.x}{(4\pi)^{2}} $

=> $\displaystyle \frac{dy}{dx} = \frac{8\pi.x}{16\pi^{2}} $

Now we can cancel out $\displaystyle 8\pi $ as it is common to both the top and bottom line.

This leaves us with $\displaystyle \frac{dy}{dx} = \frac{x}{2\pi} $ - May 1st 2010, 10:06 AMskeeter
- May 1st 2010, 10:06 AMharish21
$\displaystyle \frac{1}{4\pi} \frac{d}{dx}x^2 = \frac{1}{4 \pi} 2x = \frac{2x}{4 \pi} = \frac{x}{2 \pi}$

that is the derivative of the first expression of your term(note that this is the same as what you got from the derivative calculator).. you have to do the same to find the derivative of the second term, and add those two to get your answer.. - May 1st 2010, 10:10 AMkmjt
I see thanks (Rofl)