derivative of e^{x^{1/3}}

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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}}}

Vereinfache

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}}}

\int_{2}^{3} \frac{35}{3 - x} d x

d er i v a t i v e (s^{6} + \frac{1}{s})^{\frac{5}{2}}

\frac{\partial}{\partial y} (3 x^{2} + 8 x y + y^{2})

\int \frac{2 x + 3}{2 x + 4} d x

d er i v a t i v e p (x) = x^{3} - 5 x^{2} - 4 x + 20