What is the derivative of (e^x)^{-2} ?

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

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

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

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derivative of

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

- \frac{2}{e ^{2 x}}

Solution steps

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

Apply the chain rule:

- \frac{2}{( e ^{x} ) ^{3}} \frac{d}{d x} (e^{x})

= - \frac{2}{( e ^{x} ) ^{3}} \frac{d}{d x} (e^{x})

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

= - \frac{2}{( e ^{x} ) ^{3}} e^{x}

Simplify

- \frac{2}{( e ^{x} ) ^{3}} e^{x} : - \frac{2}{e ^{2 x}}

= - \frac{2}{e ^{2 x}}

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