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

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

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

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

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

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

Solution steps

\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}

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