Question

f(x)=(x+2017) /e^x.
Calculati derivata a doua

Answer 1

f(x) =(x+2017) *e^(-x)
f'(x) =1*e^(-x) + (x+2017) * (-1) *e^(-x)= e^(-x) (1-x-2017)=-(x+2016)* e^(-x)

f"(x) = (-1)(1*e^(-x)+(-1)(x+2016)e^(-x)=

 = (-1) (e^(-x)(1-x-2016)=
=(-1)* e^(-x) (-x-2015)=
=(x+2015)e^(-x)

Exta
Problema admite o frumoasa generalizare pt .derivatde ordin (n), emonstrabila prin inductie