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) =
=$e^{- \frac{x}{2} } + x * e^{- \frac{x}{2} } *(- \frac{1}{2})= \\ e^{- \frac{x}{2} } - \frac{x}{2} * e^{- \frac{x}{2} } = e ^{- \frac{x}{2} } (1- \frac{x}{2} )$