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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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}

\frac{1}{( s ^{2} + 2 )}

\frac{d}{d x} (lo g_{10} (1 + x^{2} y^{2}))

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

\frac{d}{d t} (15 + 20 t)

\frac{( 1 + e ^{x} )}{( 1 - e ^{x} )}

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