derivative 4e^{t/2}

Lösung

ableitung von

4 e^{\frac{t}{2}}

2 e^{\frac{t}{2}}

Schritte zur Lösung

\frac{d}{d t} (4 e^{\frac{t}{2}})

Entferne die Konstante:

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

= 4 \frac{d}{d t} (e^{\frac{t}{2}})

Wende die Kettenregel an:

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

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

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

= 4 e^{\frac{t}{2}} \frac{1}{2}

Vereinfache

4 e^{\frac{t}{2}} \frac{1}{2} : 2 e^{\frac{t}{2}}

= 2 e^{\frac{t}{2}}

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