What is the derivative of f(x)=xe^{-x} ?

The derivative of f(x)=xe^{-x} is e^{-x}-e^{-x}x

What is the first derivative of f(x)=xe^{-x} ?

The first derivative of f(x)=xe^{-x} is e^{-x}-e^{-x}x

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derivative

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

What is the derivative of f(x)=xe^{-x} ?
The derivative of f(x)=xe^{-x} is e^{-x}-e^{-x}x
What is the first derivative of f(x)=xe^{-x} ?
The first derivative of f(x)=xe^{-x} is e^{-x}-e^{-x}x