19.9k views
0 votes
Differentiate y=xe^(-x/2).

1 Answer

5 votes
We will use the product rule:
d/dx( f(x) · g(x) ) = f´( x ) g( x ) + g´( x ) f( x ) ( and after that the chain rule )
y´ = ( x ) ´· e^(-x/2) + ( e^(-x/2)´ · x) =
=
e^{- (x)/(2) } + x * e^{- (x)/(2) } *(- (1)/(2))= \\ e^{- (x)/(2) } - (x)/(2) * e^{- (x)/(2) } = e ^{- (x)/(2) } (1- (x)/(2) )
User Gmustudent
by
8.6k points

Related questions

asked Apr 9, 2024 28.5k views
Engnyl asked Apr 9, 2024
by Engnyl
8.2k points
1 answer
3 votes
28.5k views
asked Apr 17, 2017 76.8k views
Botchniaque asked Apr 17, 2017
by Botchniaque
8.1k points
1 answer
4 votes
76.8k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.