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

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

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

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

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derivative of

3 x e^{- 2 x}

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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