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Beliebt Rechnen >

derivative of 4^{ln(x})

Lösung

\frac{d}{d x} (4^{l n (x)})

Lösung

2 ln (2) x^{2 l n (2) - 1}

Schritte zur Lösung

\frac{d}{d x} (4^{l n (x)})

Wende Exponentenregel an:

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

4^{l n (x)} = e^{l n (x) l n (4)}

= \frac{d}{d x} (e^{l n (x) l n (4)})

Wende die Kettenregel an:

e^{l n (x) l n (4)} \frac{d}{d x} (ln (x) ln (4))

= e^{l n (x) l n (4)} \frac{d}{d x} (ln (x) ln (4))

\frac{d}{d x} (ln (x) ln (4)) = \frac{2 ln ( 2 )}{x}

= e^{l n (x) l n (4)} \frac{2 ln ( 2 )}{x}

Vereinfache

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

= 2 ln (2) x^{2 l n (2) - 1}

Graph

Beliebte Beispiele

integral from 0 to 1 of 2pix(15-15x)

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