What is the derivative of-4xe^{-2x^2} ?

The derivative of-4xe^{-2x^2} is -4(e^{-2x^2}-4e^{-2x^2}x^2)

What is the first derivative of-4xe^{-2x^2} ?

The first derivative of-4xe^{-2x^2} is -4(e^{-2x^2}-4e^{-2x^2}x^2)

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\frac{d}{d x} (- 4 x e^{- 2 x^{2}})

- 4 (e^{- 2 x^{2}} - 4 e^{- 2 x^{2}} x^{2})

Solution steps

\frac{d}{d x} (- 4 x e^{- 2 x^{2}})

Take the constant out:

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

= - 4 \frac{d}{d x} (x e^{- 2 x^{2}})

Apply the Product Rule:

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

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

= - 4 (\frac{d x}{d x} e^{- 2 x^{2}} + \frac{d}{d x} (e^{- 2 x^{2}}) x)

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

\frac{d}{d x} (e^{- 2 x^{2}}) = - 4 e^{- 2 x^{2}} x

= - 4 (1 \cdot e^{- 2 x^{2}} + (- 4 e^{- 2 x^{2}} x) x)

Simplify

- 4 (1 \cdot e^{- 2 x^{2}} + (- 4 e^{- 2 x^{2}} x) x) : - 4 (e^{- 2 x^{2}} - 4 e^{- 2 x^{2}} x^{2})

= - 4 (e^{- 2 x^{2}} - 4 e^{- 2 x^{2}} x^{2})

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lo g_{5} (x^{2} - 4)

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What is the derivative of-4xe^{-2x^2} ?
The derivative of-4xe^{-2x^2} is -4(e^{-2x^2}-4e^{-2x^2}x^2)
What is the first derivative of-4xe^{-2x^2} ?
The first derivative of-4xe^{-2x^2} is -4(e^{-2x^2}-4e^{-2x^2}x^2)