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

\frac{d}{d x} ((7 x^{2} - 14 x + 14) e^{x})

\int \frac{4 x ^{3} + 4 x + 4}{x ^{3} + x} d x

4 (x - \frac{1}{x})^{2}, at x = 2

f (x) = 4 x^{7} - 5 cos (x)

\int e^{x} x d 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