What is (\partial)/(\partial x)(xe^{-x}) ?

The answer to (\partial)/(\partial x)(xe^{-x}) is e^{-x}-e^{-x}x

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(\partial)/(\partial x)(xe^{-x})

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Simplify

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

\int (9 - y) y d y

n = 1 \sum \infty (cos (24))^{n}

x \to 0 lim (\frac{x ^{2}}{2} - \frac{2}{x})

f (x) = arccos (\frac{x}{2})

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

What is (\partial)/(\partial x)(xe^{-x}) ?
The answer to (\partial)/(\partial x)(xe^{-x}) is e^{-x}-e^{-x}x