What is the derivative of (3-4xe^{-2x^2}) ?

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

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

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

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\frac{d}{d x} ((3 - 4 x) e^{- 2 x^{2}})

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

Solution steps

\frac{d}{d x} ((3 - 4 x) e^{- 2 x^{2}})

Apply the Product Rule:

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

f = 3 - 4 x, g = e^{- 2 x^{2}}

= \frac{d}{d x} (3 - 4 x) e^{- 2 x^{2}} + \frac{d}{d x} (e^{- 2 x^{2}}) (3 - 4 x)

\frac{d}{d x} (3 - 4 x) = - 4

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

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

Simplify

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

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