Question

Find the 600th derivative of
f(x) = xe−x.

Answer 1

The 600th derivative of: f ( x ) = x * e^(-x)
f ` ( x ) = e^(-x) - x e^(-x)
f `` ( x ) = - e^(-x) - ( e^(-x) - x e ^(-x) ) = - 2 e^(-x) + x e^(-x)
f ``` ( x ) = 3 e^(-x) - x e^(-x)
          ....            .....
$f ^{n}(x) = ( - 1 ) ^{n}* ( x e ^{-x}- n * e ^{-x} \\ f ^{600}=(-1) ^{600}* ( x e ^{-x}-600 e ^{-x} ) \\ f ^{600}(x) = -600 e ^{-x}+x e ^{-x}$