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Beliebt Rechnen >

derivative of log_{2}(5x)

Lösung

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

Lösung

\frac{1}{ln ( 2 ) x}

Schritte zur Lösung

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

Wende die log Regel an:

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

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

\frac{1}{5 x} \frac{d}{d x} (5 x)

= \frac{1}{5 x} \frac{d}{d x} (5 x)

\frac{d}{d x} (5 x) = 5

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

Vereinfache

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

= \frac{1}{ln ( 2 ) x}

Graph

Beliebte Beispiele

integral of (3+2x^2)/(x^2)

\int \frac{3 + 2 x ^{2}}{x ^{2}} d x

derivative of (10/(x^3))

\frac{d}{d x} (\frac{10}{x ^{3}})

inverselaplace 7/(4s-12)

in v erse l a pl a ce \frac{7}{4 s - 12}

integral of sin^2(x)cos^2(x)

\int sin^{2} (x) cos^{2} (x) d x

derivative of pi/(x^{18})

\frac{d}{d x} (\frac{π}{x ^{18}})