What is the derivative of (5-e^{-4x})^4 ?

The derivative of (5-e^{-4x})^4 is 16e^{-4x}(5-e^{-4x})^3

What is the first derivative of (5-e^{-4x})^4 ?

The first derivative of (5-e^{-4x})^4 is 16e^{-4x}(5-e^{-4x})^3

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derivative of

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

16 e^{- 4 x} (5 - e^{- 4 x})^{3}

Solution steps

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

Apply the chain rule:

4 (5 - e^{- 4 x})^{3} \frac{d}{d x} (5 - e^{- 4 x})

= 4 (5 - e^{- 4 x})^{3} \frac{d}{d x} (5 - e^{- 4 x})

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

= 4 (5 - e^{- 4 x})^{3} \cdot 4 e^{- 4 x}

Simplify

= 16 e^{- 4 x} (5 - e^{- 4 x})^{3}

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What is the derivative of (5-e^{-4x})^4 ?
The derivative of (5-e^{-4x})^4 is 16e^{-4x}(5-e^{-4x})^3
What is the first derivative of (5-e^{-4x})^4 ?
The first derivative of (5-e^{-4x})^4 is 16e^{-4x}(5-e^{-4x})^3