Suppose That You Are Told That the Taylor Series Of f(x)=e^{-x^{2}}

Short Answer

Suppose that you are told that the Taylor series of $f(x)=e^{-x^{2}}$ about x = 0 is $1-\frac{x^{2}}{1 !}+\frac{x^{4}}{2 !}-\frac{x^{6}}{3 !}+\cdots$ .Find $\left.\frac{d^{2}}{d^{2}}\left(e^{-x^{2}}\right)\right|_{x=0}$ .