What is the derivative of e^{-2/3 x} ?

The derivative of e^{-2/3 x} is -2/3 e^{-(2x)/3}

What is the first derivative of e^{-2/3 x} ?

The first derivative of e^{-2/3 x} is -2/3 e^{-(2x)/3}

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

- \frac{2}{3} e^{- \frac{2 x}{3}}

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

What is the derivative of e^{-2/3 x} ?
The derivative of e^{-2/3 x} is -2/3 e^{-(2x)/3}
What is the first derivative of e^{-2/3 x} ?
The first derivative of e^{-2/3 x} is -2/3 e^{-(2x)/3}