Let us first find the first derivative of #f(x)=e^x/x^2# using quotient rule
that if #f(x)=(g(x))/(h(x))#
then #(df)/(dx)=((dg)/(dx)xxh(x)-(dh)/(dx)xxg(x))/(h(x))^2# .
#(df)/(dx)=(x^2xxe^x-e^x xx2x)/(x^2)^2=(x^2e^x-2xe^x)/x^4=(xe^x(x-2))/x^4=(e^x(x-2))/x^3#
and second derivative #(d^2f)/(dx^2)=d/(dx)((df)/(dx))=d/(dx)(e^x(x-2))/x^3#
= #(x^3xx(e^x(x-2)+e^x xx1)-e^x(x-2)xx3x^2)/x^6#
= #(e^x x^3(x-2)+e^x x^3-3x^2e^x(x-2))/x^6#
= #(e^x x^2(x(x-2)+x-3(x-2)))/x^6#
= #(e^x(x^2-2x+x-3x+6))/x^4#
= #(e^x(x^2-4x+6))/x^4#
