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

The derivative of 5(e^x)^{-4} is -(20)/(e^{4x)}

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

The first derivative of 5(e^x)^{-4} is -(20)/(e^{4x)}

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derivative of

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

- \frac{20}{e ^{4 x}}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

5 (- \frac{4}{( e ^{x} ) ^{5}} e^{x}) : - \frac{20}{e ^{4 x}}

= - \frac{20}{e ^{4 x}}

What is the derivative of 5(e^x)^{-4} ?
The derivative of 5(e^x)^{-4} is -(20)/(e^{4x)}
What is the first derivative of 5(e^x)^{-4} ?
The first derivative of 5(e^x)^{-4} is -(20)/(e^{4x)}