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

The derivative of-xe^{-x}+e^{-x} is e^{-x}x-2e^{-x}

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

The first derivative of-xe^{-x}+e^{-x} is e^{-x}x-2e^{-x}

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derivative of

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

e^{- x} x - 2 e^{- x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= - (e^{- x} - e^{- x} x) - e^{- x}

Simplify

= e^{- x} x - 2 e^{- x}

What is the derivative of-xe^{-x}+e^{-x} ?
The derivative of-xe^{-x}+e^{-x} is e^{-x}x-2e^{-x}
What is the first derivative of-xe^{-x}+e^{-x} ?
The first derivative of-xe^{-x}+e^{-x} is e^{-x}x-2e^{-x}