What is the derivative of e^{-x}+xe^{-x} ?

The derivative of e^{-x}+xe^{-x} is -e^{-x}x

What is the first derivative of e^{-x}+xe^{-x} ?

The first derivative of e^{-x}+xe^{-x} is -e^{-x}x

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\frac{d}{d x} (e^{- x} + x e^{- x})

- e^{- x} x

Solution steps

\frac{d}{d x} (e^{- x} + x e^{- x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{- x}) + \frac{d}{d x} (x e^{- x})

\frac{d}{d x} (e^{- x}) = - e^{- x}

\frac{d}{d x} (x e^{- x}) = e^{- x} - e^{- x} x

= - e^{- x} + e^{- x} - e^{- x} x

Simplify

= - e^{- x} x

What is the derivative of e^{-x}+xe^{-x} ?
The derivative of e^{-x}+xe^{-x} is -e^{-x}x
What is the first derivative of e^{-x}+xe^{-x} ?
The first derivative of e^{-x}+xe^{-x} is -e^{-x}x