derivative of x^{log_{6}(x})

Lösung

\frac{d}{d x} (x^{l o g_{6} (x)})

\frac{2 x ^{l o g_{6} (x) - 1} ln ( x )}{ln ( 6 )}

Schritte zur Lösung

\frac{d}{d x} (x^{l o g_{6} (x)})

Wende Exponentenregel an:

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

x^{l o g_{6} (x)} = e^{l o g_{6} (x) l n (x)}

= \frac{d}{d x} (e^{l o g_{6} (x) l n (x)})

Wende die Kettenregel an:

e^{l o g_{6} (x) l n (x)} \frac{d}{d x} (lo g_{6} (x) ln (x))

= e^{l o g_{6} (x) l n (x)} \frac{d}{d x} (lo g_{6} (x) ln (x))

\frac{d}{d x} (lo g_{6} (x) ln (x)) = \frac{2 ln ( x )}{ln ( 6 ) x}

= e^{l o g_{6} (x) l n (x)} \frac{2 ln ( x )}{ln ( 6 ) x}

Vereinfache

e^{l o g_{6} (x) l n (x)} \frac{2 ln ( x )}{ln ( 6 ) x} : \frac{2 x ^{l o g_{6} (x) - 1} ln ( x )}{ln ( 6 )}

= \frac{2 x ^{l o g_{6} (x) - 1} ln ( x )}{ln ( 6 )}

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