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

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

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

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

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

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

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