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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

= 2 (1 \cdot e^{- 4 x} + (- 4 e^{- 4 x}) x)

Simplify

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

y = sin (3 x) + cos (8 x)

\frac{d}{d x} (cos (3 x))

\frac{d}{d x} (arcsin (x) + arccos (x))

x \to 2 - lim (2 x)

\int 8 x + 1 d x

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