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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- x}, g = x

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

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

\frac{d x}{d x} = 1

= - ((- e^{- x}) x + 1 \cdot e^{- x})

Simplify

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

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