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Beliebt Rechnen >

derivative of 10^{2x-1}

Lösung

\frac{d}{d x} (1 0^{2 x - 1})

Lösung

ln (10) \cdot 4^{x} \cdot 5^{2 x - 1}

Schritte zur Lösung

\frac{d}{d x} (1 0^{2 x - 1})

Wende Exponentenregel an:

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

1 0^{2 x - 1} = e^{(2 x - 1) l n (10)}

= \frac{d}{d x} (e^{(2 x - 1) l n (10)})

Wende die Kettenregel an:

e^{(2 x - 1) l n (10)} \frac{d}{d x} ((2 x - 1) ln (10))

= e^{(2 x - 1) l n (10)} \frac{d}{d x} ((2 x - 1) ln (10))

\frac{d}{d x} ((2 x - 1) ln (10)) = 2 ln (10)

= e^{(2 x - 1) l n (10)} \cdot 2 ln (10)

Vereinfache

e^{(2 x - 1) l n (10)} \cdot 2 ln (10) : ln (10) \cdot 4^{x} \cdot 5^{2 x - 1}

= ln (10) \cdot 4^{x} \cdot 5^{2 x - 1}

Graph

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