Most certainly not! You're going to have to use the chain rule every time, which is going to result in some polynomail times [itex]e^{ax^2}[/itex]. In fact, the result is going to be related to the Hermite polynomials, defined byThe answer to this question would most probably be (2xa)^n*(e)^a(x)^2
We define a new variable u = i sqrt(a) x:I am looking a formula to compute the derivitative of [tex]e^{a x^2}[/tex] with respect to x n times, where a is a constant.
[tex]\frac{d^n}{dx^n}e^{a x^2}[/tex]
I am going to find the result of above derivitative when x -> 0.