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

The derivative of-2(e^{-x^2}-2e^{-x^2}x^2) is -2(4e^{-x^2}x^3-6e^{-x^2}x)

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

The first derivative of-2(e^{-x^2}-2e^{-x^2}x^2) is -2(4e^{-x^2}x^3-6e^{-x^2}x)

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

- 2 (4 e^{- x^{2}} x^{3} - 6 e^{- x^{2}} x)

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (2 e^{- x^{2}} x^{2}) = 2 (- 2 e^{- x^{2}} x^{3} + 2 e^{- x^{2}} x)

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

Expand

- 2 e^{- x^{2}} x - 2 (- 2 e^{- x^{2}} x^{3} + 2 e^{- x^{2}} x) : 4 e^{- x^{2}} x^{3} - 6 e^{- x^{2}} x

= - 2 (4 e^{- x^{2}} x^{3} - 6 e^{- x^{2}} x)

What is the derivative of-2(e^{-x^2}-2e^{-x^2}x^2) ?
The derivative of-2(e^{-x^2}-2e^{-x^2}x^2) is -2(4e^{-x^2}x^3-6e^{-x^2}x)
What is the first derivative of-2(e^{-x^2}-2e^{-x^2}x^2) ?
The first derivative of-2(e^{-x^2}-2e^{-x^2}x^2) is -2(4e^{-x^2}x^3-6e^{-x^2}x)