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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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