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)

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}

\int_{0}^{9} 2 π y (\frac{y}{3}) d y

e^{\frac{x}{x - 4}}

\frac{8 s + 2}{s ^{2} - 25}

\frac{d y}{d x} + x^{2} y = x^{2}

n = 1 \sum \infty \frac{4}{7 ^{n}} + \frac{3}{n}

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}