What is the derivative of xe^{-x/4} ?

The derivative of xe^{-x/4} is e^{-x/4}-(e^{-x/4}x)/4

What is the first derivative of xe^{-x/4} ?

The first derivative of xe^{-x/4} is e^{-x/4}-(e^{-x/4}x)/4

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\frac{d}{d x} (x e^{- \frac{x}{4}})

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

Solution steps

\frac{d}{d x} (x e^{- \frac{x}{4}})

Apply the Product Rule:

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

f = x, g = e^{- \frac{x}{4}}

= \frac{d x}{d x} e^{- \frac{x}{4}} + \frac{d}{d x} (e^{- \frac{x}{4}}) x

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

\frac{d}{d x} (e^{- \frac{x}{4}}) = - \frac{1}{4} e^{- \frac{x}{4}}

= 1 \cdot e^{- \frac{x}{4}} + (- \frac{1}{4} e^{- \frac{x}{4}}) x

Simplify

1 \cdot e^{- \frac{x}{4}} + (- \frac{1}{4} e^{- \frac{x}{4}}) x : e^{- \frac{x}{4}} - \frac{e ^{- \frac{x}{4}} x}{4}

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

\frac{d}{d x} (\frac{y}{y - x})

\frac{d}{d x} (e^{5 x + 1} arccsch (x + 1))

n = 1 \sum \infty \frac{2}{3 ^{2 n}}

\frac{d}{d x} (\frac{11}{x})

What is the derivative of xe^{-x/4} ?
The derivative of xe^{-x/4} is e^{-x/4}-(e^{-x/4}x)/4
What is the first derivative of xe^{-x/4} ?
The first derivative of xe^{-x/4} is e^{-x/4}-(e^{-x/4}x)/4