What is the derivative of x^2e^{-x^2} ?

The derivative of x^2e^{-x^2} is 2e^{-x^2}x-2e^{-x^2}x^3

What is the first derivative of x^2e^{-x^2} ?

The first derivative of x^2e^{-x^2} is 2e^{-x^2}x-2e^{-x^2}x^3

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derivative of

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

2 e^{- x^{2}} x - 2 e^{- x^{2}} x^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x e^{- x^{2}} + (- 2 e^{- x^{2}} x) x^{2} : 2 e^{- x^{2}} x - 2 e^{- x^{2}} x^{3}

= 2 e^{- x^{2}} x - 2 e^{- x^{2}} x^{3}

What is the derivative of x^2e^{-x^2} ?
The derivative of x^2e^{-x^2} is 2e^{-x^2}x-2e^{-x^2}x^3
What is the first derivative of x^2e^{-x^2} ?
The first derivative of x^2e^{-x^2} is 2e^{-x^2}x-2e^{-x^2}x^3