What is the derivative of (e^x)^{-1} ?

The derivative of (e^x)^{-1} is -1/(e^x)

What is the first derivative of (e^x)^{-1} ?

The first derivative of (e^x)^{-1} is -1/(e^x)

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derivative of

(e^{x})^{- 1}

- \frac{1}{e ^{x}}

Solution steps

\frac{d}{d x} ((e^{x})^{- 1})

Apply the chain rule:

- \frac{1}{( e ^{x} ) ^{2}} \frac{d}{d x} (e^{x})

= - \frac{1}{( e ^{x} ) ^{2}} \frac{d}{d x} (e^{x})

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

= - \frac{1}{( e ^{x} ) ^{2}} e^{x}

Simplify

- \frac{1}{( e ^{x} ) ^{2}} e^{x} : - \frac{1}{e ^{x}}

= - \frac{1}{e ^{x}}

What is the derivative of (e^x)^{-1} ?
The derivative of (e^x)^{-1} is -1/(e^x)
What is the first derivative of (e^x)^{-1} ?
The first derivative of (e^x)^{-1} is -1/(e^x)