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Beliebt Rechnen >

d/(dt)(10^{2sqrt(t)})

Lösung

\frac{d}{d t} (1 0^{2 t})

Lösung

\frac{ln ( 10 ) \cdot 10 0 ^{t}}{t}

Schritte zur Lösung

\frac{d}{d t} (1 0^{2 t})

Vereinfache

1 0^{2 t} : 10 0^{t}

= \frac{d}{d t} (10 0^{t})

Wende Exponentenregel an:

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

10 0^{t} = e^{t l n (100)}

= \frac{d}{d t} (e^{t l n (100)})

Wende die Kettenregel an:

e^{t l n (100)} \frac{d}{d t} (t ln (100))

= e^{t l n (100)} \frac{d}{d t} (t ln (100))

\frac{d}{d t} (t ln (100)) = \frac{ln ( 10 )}{t}

= e^{t l n (100)} \frac{ln ( 10 )}{t}

Vereinfache

e^{t l n (100)} \frac{ln ( 10 )}{t} : \frac{ln ( 10 ) \cdot 10 0 ^{t}}{t}

= \frac{ln ( 10 ) \cdot 10 0 ^{t}}{t}

Graph

Beliebte Beispiele

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