Question

Differentiate y=xe^(-x/2).

Answer 1

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) )`