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

The derivative of e^{-4x}-4e^{-4x}x is 16e^{-4x}x-8e^{-4x}

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

The first derivative of e^{-4x}-4e^{-4x}x is 16e^{-4x}x-8e^{-4x}

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

16 e^{- 4 x} x - 8 e^{- 4 x}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

- 4 e^{- 4 x} - 4 (- 4 e^{- 4 x} x + e^{- 4 x}) : 16 e^{- 4 x} x - 8 e^{- 4 x}

= 16 e^{- 4 x} x - 8 e^{- 4 x}

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What is the derivative of e^{-4x}-4e^{-4x}x ?
The derivative of e^{-4x}-4e^{-4x}x is 16e^{-4x}x-8e^{-4x}
What is the first derivative of e^{-4x}-4e^{-4x}x ?
The first derivative of e^{-4x}-4e^{-4x}x is 16e^{-4x}x-8e^{-4x}