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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

Simplify

- 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

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

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