What is the derivative of e^{-x/5} ?

The derivative of e^{-x/5} is -1/5 e^{-x/5}

What is the first derivative of e^{-x/5} ?

The first derivative of e^{-x/5} is -1/5 e^{-x/5}

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

- \frac{1}{5} e^{- \frac{x}{5}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (- \frac{x}{5}) = - \frac{1}{5}

= e^{- \frac{x}{5}} (- \frac{1}{5})

Simplify

= - \frac{1}{5} e^{- \frac{x}{5}}

What is the derivative of e^{-x/5} ?
The derivative of e^{-x/5} is -1/5 e^{-x/5}
What is the first derivative of e^{-x/5} ?
The first derivative of e^{-x/5} is -1/5 e^{-x/5}