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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

y = 1 1^{x}

\frac{d}{d x} (\frac{5}{x ^{\frac{1}{3}}})

\frac{\partial}{\partial x} (2 x e^{x^{2} - y^{2}})

x \to 0 lim (x (1 - \frac{1}{x}))

\frac{d ^{2}}{d x ^{2}} f (x) = 4 x^{5} - \frac{3}{x ^{2}}

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