What is the derivative of (x-1e^{-x}) ?

The derivative of (x-1e^{-x}) is -e^{-x}x+2e^{-x}

What is the first derivative of (x-1e^{-x}) ?

The first derivative of (x-1e^{-x}) is -e^{-x}x+2e^{-x}

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\frac{d}{d x} ((x - 1) e^{- x})

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

Solution steps

\frac{d}{d x} ((x - 1) e^{- x})

Apply the Product Rule:

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

f = x - 1, g = e^{- x}

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

\frac{d}{d x} (x - 1) = 1

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

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

Simplify

1 \cdot e^{- x} + (- e^{- x}) (x - 1) : - e^{- x} x + 2 e^{- x}

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

What is the derivative of (x-1e^{-x}) ?
The derivative of (x-1e^{-x}) is -e^{-x}x+2e^{-x}
What is the first derivative of (x-1e^{-x}) ?
The first derivative of (x-1e^{-x}) is -e^{-x}x+2e^{-x}