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

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

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

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

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derivative of

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

- 2 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

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

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

x \to 0 lim (- x + 1)

x^{^{'}} = x^{2}, x (0) = - 1

\frac{d}{d x} (\frac{x ^{2}}{100})

\int 5 x^{8} d x

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