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

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

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

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

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

e^{- x} x - 2 e^{- 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} x) + \frac{d}{d x} (e^{- x})

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

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

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

Simplify

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

y^{^{'}} = y^{2} - 100

\frac{\partial}{\partial y} (2 y^{2} e^{x y^{2}})

\int_{- \infty}^{0} x e^{- 8 x} d x

arctan (x - 1 + x^{2})

f (x) = x^{5} - 5 x^{3} + x - 1

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