What is the derivative of 1/(e^y) ?

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

What is the first derivative of 1/(e^y) ?

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

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derivative of

\frac{1}{e ^{y}}

- e^{- y}

Solution steps

\frac{d}{d y} (\frac{1}{e ^{y}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d y} (e^{- y})

Apply the chain rule:

e^{- y} \frac{d}{d y} (- y)

= e^{- y} \frac{d}{d y} (- y)

\frac{d}{d y} (- y) = - 1

= e^{- y} (- 1)

Simplify

= - e^{- y}

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