What is the derivative of (e^x)^{1/3} ?

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

What is the first derivative of (e^x)^{1/3} ?

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

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derivative of

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

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

Solution steps

\frac{d}{d x} ((e^{x})^{\frac{1}{3}})

Simplify

(e^{x})^{\frac{1}{3}} : e^{\frac{x}{3}}

= \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}

d er i v a t i v e \frac{1}{( s ^{2} + 2 )}

\frac{d}{d t} (t^{3} - 6 t^{2} + 9 t)

d er i v a t i v e \frac{( 1 + e ^{x} )}{( 1 - e ^{x} )}

d er i v a t i v e 5 x^{6}

d er i v a t i v e 2 e^{3} t sin (2 t)

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