derivative of 12e^{x/2}

Lösung

\frac{d}{d x} (12 e^{\frac{x}{2}})

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

Schritte zur Lösung

\frac{d}{d x} (12 e^{\frac{x}{2}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 12 \frac{d}{d x} (e^{\frac{x}{2}})

Wende die Kettenregel an:

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

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

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

= 12 e^{\frac{x}{2}} \frac{1}{2}

Vereinfache

12 e^{\frac{x}{2}} \frac{1}{2} : 6 e^{\frac{x}{2}}

= 6 e^{\frac{x}{2}}

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