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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\frac{d}{d x} (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}

n = 1 \sum \infty n 3^{- n}

x \to 0 lim (\frac{1}{3 x})

x y^{^{'}} - y = x ln (x)

4^{x} x^{4}

x (x + 1) (\frac{d y}{d x}) + x y = 1

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}