What is the derivative of e^{-x/3} ?

The derivative of e^{-x/3} is -1/3 e^{-x/3}

What is the first derivative of e^{-x/3} ?

The first derivative of e^{-x/3} is -1/3 e^{-x/3}

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

- \frac{1}{3} e^{- \frac{x}{3}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (- \frac{x}{3}) = - \frac{1}{3}

= e^{- \frac{x}{3}} (- \frac{1}{3})

Simplify

= - \frac{1}{3} e^{- \frac{x}{3}}

What is the derivative of e^{-x/3} ?
The derivative of e^{-x/3} is -1/3 e^{-x/3}
What is the first derivative of e^{-x/3} ?
The first derivative of e^{-x/3} is -1/3 e^{-x/3}