Question 998455


How does {{{x^2(-e^(-x))+e^(-x)(2x)}}} simplify down to {{{xe^(-x)(2-x)}}}:



{{{x^2(-e^(-x))+e^(-x)(2x)}}}......first write {{{e^(-x)}}} as {{{1/(e^x))

{{{x^2(-(1/e^x))+(1/e^x)(2x)}}}

= {{{-(x^2/e^x)+(2x/e^x)}}}

= {{{-(x^2+2x)/e^x}}}

= {{{(-1)(x^2+2x)/e^x}}}

= {{{(2x-x^2)/e^x}}}

={{{ (x(2-x))(1/e^x)}}}.........write {{{1/e^x}}} as {{{e^(-x)}}}

= {{{x(2-x)*e^x^-1}}}