What is the derivative of x^2e^{(-x/(10)}) ?

The derivative of x^2e^{(-x/(10)}) is -(e^{-x/(10)}x^2)/(10)+2e^{-x/(10)}x

What is the first derivative of x^2e^{(-x/(10)}) ?

The first derivative of x^2e^{(-x/(10)}) is -(e^{-x/(10)}x^2)/(10)+2e^{-x/(10)}x

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\frac{d}{d x} (x^{2} e^{\frac{- x}{10}})

- \frac{e ^{- \frac{x}{10}} x ^{2}}{10} + 2 e^{- \frac{x}{10}} x

Solution steps

\frac{d}{d x} (x^{2} e^{\frac{- x}{10}})

Simplify

x^{2} e^{\frac{- x}{10}} : e^{- \frac{x}{10}} x^{2}

= \frac{d}{d x} (e^{- \frac{x}{10}} x^{2})

Apply the Product Rule:

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

f = e^{- \frac{x}{10}}, g = x^{2}

= \frac{d}{d x} (e^{- \frac{x}{10}}) x^{2} + \frac{d}{d x} (x^{2}) e^{- \frac{x}{10}}

\frac{d}{d x} (e^{- \frac{x}{10}}) = - \frac{1}{10} e^{- \frac{x}{10}}

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

= (- \frac{1}{10} e^{- \frac{x}{10}}) x^{2} + 2 x e^{- \frac{x}{10}}

Simplify

(- \frac{1}{10} e^{- \frac{x}{10}}) x^{2} + 2 x e^{- \frac{x}{10}} : - \frac{e ^{- \frac{x}{10}} x ^{2}}{10} + 2 e^{- \frac{x}{10}} x

= - \frac{e ^{- \frac{x}{10}} x ^{2}}{10} + 2 e^{- \frac{x}{10}} x

What is the derivative of x^2e^{(-x/(10)}) ?
The derivative of x^2e^{(-x/(10)}) is -(e^{-x/(10)}x^2)/(10)+2e^{-x/(10)}x
What is the first derivative of x^2e^{(-x/(10)}) ?
The first derivative of x^2e^{(-x/(10)}) is -(e^{-x/(10)}x^2)/(10)+2e^{-x/(10)}x