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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\frac{d}{d x} (x^{6} (x - 4)^{5})

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\frac{d}{d x} (ln (3 + 4 x))

\int tan^{3} (4 x) sec^{2} (4 x) d x

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