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

The derivative of e^{x^{1/3}} is (e^{x^{1/3}})/(3x^{2/3)}

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

The first derivative of e^{x^{1/3}} is (e^{x^{1/3}})/(3x^{2/3)}

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

\frac{e ^{x^{\frac{1}{3}}}}{3 x ^{\frac{2}{3}}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{\frac{1}{3}}) = \frac{1}{3 x ^{\frac{2}{3}}}

= e^{x^{\frac{1}{3}}} \frac{1}{3 x ^{\frac{2}{3}}}

Simplify

e^{x^{\frac{1}{3}}} \frac{1}{3 x ^{\frac{2}{3}}} : \frac{e ^{x^{\frac{1}{3}}}}{3 x ^{\frac{2}{3}}}

= \frac{e ^{x^{\frac{1}{3}}}}{3 x ^{\frac{2}{3}}}

What is the derivative of e^{x^{1/3}} ?
The derivative of e^{x^{1/3}} is (e^{x^{1/3}})/(3x^{2/3)}
What is the first derivative of e^{x^{1/3}} ?
The first derivative of e^{x^{1/3}} is (e^{x^{1/3}})/(3x^{2/3)}