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Beliebt Rechnen >

derivative log_{6}(x^2-5x)

Lösung

ableitung von

lo g_{6} (x^{2} - 5 x)

Lösung

\frac{2 x - 5}{ln ( 6 ) ( x ^{2} - 5 x )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{6} (x^{2} - 5 x))

Wende die log Regel an:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( x ^{2} - 5 x )}{ln ( 6 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 6 )} \frac{d}{d x} (ln (x^{2} - 5 x))

Wende die Kettenregel an:

\frac{1}{x ^{2} - 5 x} \frac{d}{d x} (x^{2} - 5 x)

= \frac{1}{x ^{2} - 5 x} \frac{d}{d x} (x^{2} - 5 x)

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

= \frac{1}{ln ( 6 )} \cdot \frac{1}{x ^{2} - 5 x} (2 x - 5)

Vereinfache

\frac{1}{ln ( 6 )} \cdot \frac{1}{x ^{2} - 5 x} (2 x - 5) : \frac{2 x - 5}{ln ( 6 ) ( x ^{2} - 5 x )}

= \frac{2 x - 5}{ln ( 6 ) ( x ^{2} - 5 x )}

Graph

Beliebte Beispiele

integral from 0 to pi/3 of 7sec^2(x)

\int_{0}^{\frac{π}{3}} 7 sec^{2} (x) d x

(\partial)/(\partial x)(3ln(x))

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fläche (sqrt(x+6)),x,-2,3

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\int sec^{6} (x) tan (x) d x

derivative y=sqrt(ln(7x))

d er i v a t i v e y = ln (7 x)