Can't remember how to differentiate this

[rainbojedi]

for my Schrödinger equation I need the second derivative of this: Axe^(-x^2/ L^2)
I think that I am missing some chain rule or something.



The solutions say: ( 4Ax^3-6AxL^2)(1/L^4)e^(-x^2/ L^2)


I only got -2Axe^(-x^2/L^2) for the 1st deriv. and 4Axe^(-x^2/L^2) and I still can't figure out what I'm missing even by looking at the solutions.

 

[Dick]

I think you are missing both the product rule and the chain rule. I'm not even sure what rule you are using. Warm up by taking the derivative of x*exp(-x^2). You should get exp(-x^2)-2*x^2*exp(-x^2). I think you may need to crack a first year calc text before dealing with the SE.

 

[Mindscrape]

Your first derivative is immediately wrong because you didn't use the product rule (but you also forgot chain rule).

 

[rainbojedi]

Thank you, your were both very right. I had immediately missed the product rule. Thanks for the help.