Prove formula from Slide $32$:

$gra{d}^{2}G(x,y)=(\frac{x^2+y^2-2{}^2}{{}^4})e^{-\frac{x^2+y^2}{2{}^2}}$

$(Basedon$ upper formula $of$ Gaussian function, Slide $32,$ and definition $of$ Laplacian, Slide $16.)$

Slide $16$ and Slide $32$ are shown $in$ the following images.