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# Differentiation watch

1. Does anyone know the formula for differentiating

n times?

Thank you!
2. (Original post by Goldenratio)
Does anyone know the formula for differentiating

n times?

Thank you!
There isn't a particularly 'nice' solution. Try looking at http://mathworld.wolfram.com/LegendrePolynomial.html (Rodrigues representation).
3. Hmm

Maybe im being stupid but

let be the ath derivative.

As a sidenote Mathworld bloody scares me. Whenever i go look something up theres just reems and reems of complicated maths.
4. (Original post by insparato)
Hmm

Maybe im being stupid but

let be the a th derivative.

Yeah. You might want to check those (product rule )
5. Oh bugger haha. School boy error of the day. I think i'll leave that up for sheer comedy.

Leibniz rule ?
6. (Original post by insparato)
Oh bugger haha. School boy error of the day. I think i'll leave that up for sheer comedy.

Leibniz rule ?
Don't worry. I did the same thing at first . Needless to say, there was a lot of crossing out and swearing involved.

You can find a series solution with the binomial theorem.
7. (Original post by insparato)
Oh bugger haha. School boy error of the day. I think i'll leave that up for sheer comedy.

Leibniz rule ?
You can use that to get a recurrence relation (I think), but again, you won't end up with a nice closed form solution.

Edit: SsEe and I may have different definitions of 'nice' here.
8. hmmm

Leibniz's general rule for products says (f.g)^n

Yes! Rodrigues' Formula was precisely where i got this from, as I was asked to compute the 4th Legendre polynomial. I thought I was just doing work for the sake of it, until you reassured me that there wasn't a simple Leibniz formula for it

I end up with a 'rough' working of
let's just say at least it has a quartic in it somewhere lol

The formula I was using
9. From what i recall from the textbook ive got.

If y = uv

10. As SsEe says, simplest is to expand first.

So

So
11. WOW you guys surely know your maths
12. (Original post by DFranklin)
As SsEe says, simplest is to expand first.

So

So
Wizz Kid!

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