Question

expression for nth derivative of e^x^2

Answer 1

Well, it's got e^x^2 in it......:-)

Answer 2

\[e ^{x ^{2}}\]

Answer 3

Then you have a polynomial multiplier

Answer 4

2x,4x^2+1,8x^3+12x,16x^4+48x^2+12,32x^5+160x^3+120x.....

Answer 5

do the first 3 derivatives and see if you can spot a pattern
\[f'(x) = 2x e^{x^{2}}\]
\[f''(x) = (2x)^{2} e^{x^{2}} + 2e^{x^{2}}\]
\[f'''(x) = (2x)^{3}e^{x^{2}} + 12x e^{x^{2}}\]
\[\rightarrow f^{n} (x) = (2x)^{n} e^{x^{2}} + ...\]

Answer 6

didn't spot, that's why ask, :)

Answer 7

http://bbs.stardestroyer.net/viewtopic.php?f=5&t=134391&view=next

Answer 8

maybe i am dumb, but i don't get it @estudier

Answer 9

Did you look up Hermite polynomials? http://en.wikipedia.org/wiki/Hermite_polynomials

There is a table in the middle of the page seems very similar looking to sequence.....

Answer 10

I have to find it without use of Hermite

Answer 11

should be simple enough, :)