Question

Найти d y и d^2 y. y=x•e^-x

Answer 1

 y=x*e^-x=x/e^x
y'=(u/v)'=1/v²*[u'v-v'u]   u=x  u'=1     v=e^x    v'=e^x
y'=1/(e^x)²[e^x-xe^x]=[1-x]/(e^x)
u=1-x   u'=-1     v=(e^x)    v'=e^x
y''=1/(e^x)²[-e^x-(1-x)e^x]  = -x/e^x