derivative of e^{x^{1/2}}

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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