What is the derivative of xe^{-x}-e^{-3} ?

The derivative of xe^{-x}-e^{-3} is -e^{-x}x+e^{-x}

What is the first derivative of xe^{-x}-e^{-3} ?

The first derivative of xe^{-x}-e^{-3} is -e^{-x}x+e^{-x}

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\frac{d}{d x} (x e^{- x} - e^{- 3})

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

Solution steps

\frac{d}{d x} (x e^{- x} - e^{- 3})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x e^{- x}) - \frac{d}{d x} (e^{- 3})

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

\frac{d}{d x} (e^{- 3}) = 0

= e^{- x} - e^{- x} x - 0

Simplify

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

What is the derivative of xe^{-x}-e^{-3} ?
The derivative of xe^{-x}-e^{-3} is -e^{-x}x+e^{-x}
What is the first derivative of xe^{-x}-e^{-3} ?
The first derivative of xe^{-x}-e^{-3} is -e^{-x}x+e^{-x}