What is (\partial)/(\partial x)(x^2e^{-x}) ?

The answer to (\partial)/(\partial x)(x^2e^{-x}) is 2e^{-x}x-e^{-x}x^2

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(\partial)/(\partial x)(x^2e^{-x})

\frac{\partial}{\partial x} (x^{2} e^{- x})

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

Solution steps

\frac{\partial}{\partial x} (x^{2} e^{- x})

Apply the Product Rule:

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

f = x^{2}, g = e^{- x}

= \frac{\partial}{\partial x} (x^{2}) e^{- x} + \frac{\partial}{\partial x} (e^{- x}) x^{2}

\frac{\partial}{\partial x} (x^{2}) = 2 x

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

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

Simplify

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

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What is (\partial)/(\partial x)(x^2e^{-x}) ?
The answer to (\partial)/(\partial x)(x^2e^{-x}) is 2e^{-x}x-e^{-x}x^2