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

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

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

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

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\frac{d}{d x} (- 6 e^{- 3 x^{2}} x)

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

Solution steps

\frac{d}{d x} (- 6 e^{- 3 x^{2}} x)

Take the constant out:

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

= - 6 \frac{d}{d x} (e^{- 3 x^{2}} x)

Apply the Product Rule:

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

f = e^{- 3 x^{2}}, g = x

= - 6 (\frac{d}{d x} (e^{- 3 x^{2}}) x + \frac{d x}{d x} e^{- 3 x^{2}})

\frac{d}{d x} (e^{- 3 x^{2}}) = - 6 e^{- 3 x^{2}} x

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

= - 6 ((- 6 e^{- 3 x^{2}} x) x + 1 \cdot e^{- 3 x^{2}})

Simplify

- 6 ((- 6 e^{- 3 x^{2}} x) x + 1 \cdot e^{- 3 x^{2}}) : - 6 (- 6 e^{- 3 x^{2}} x^{2} + e^{- 3 x^{2}})

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

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