derivative 5*2^{sqrt(t-2)}

Lösung

ableitung von

5 \cdot 2^{t - 2}

\frac{5 ln ( 2 ) \cdot 2 ^{t - 2 - 1}}{t - 2}

Schritte zur Lösung

\frac{d}{d t} (5 \cdot 2^{t - 2})

Entferne die Konstante:

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

= 5 \frac{d}{d t} (2^{t - 2})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

2^{t - 2} = e^{t - 2 l n (2)}

= 5 \frac{d}{d t} (e^{t - 2 l n (2)})

Wende die Kettenregel an:

e^{t - 2 l n (2)} \frac{d}{d t} (t - 2 ln (2))

= e^{t - 2 l n (2)} \frac{d}{d t} (t - 2 ln (2))

\frac{d}{d t} (t - 2 ln (2)) = \frac{ln ( 2 )}{2 t - 2}

= 5 e^{t - 2 l n (2)} \frac{ln ( 2 )}{2 t - 2}

Vereinfache

5 e^{t - 2 l n (2)} \frac{ln ( 2 )}{2 t - 2} : \frac{5 ln ( 2 ) \cdot 2 ^{t - 2 - 1}}{t - 2}

= \frac{5 ln ( 2 ) \cdot 2 ^{t - 2 - 1}}{t - 2}

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