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Beliebt Rechnen >

derivative of log_{10}(2x-3)

Lösung

\frac{d}{d x} (lo g_{10} (2 x - 3))

Lösung

\frac{2}{ln ( 10 ) ( 2 x - 3 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{10} (2 x - 3))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( 2 x - 3 )}{ln ( 10 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (2 x - 3))

Wende die Kettenregel an:

\frac{1}{2 x - 3} \frac{d}{d x} (2 x - 3)

= \frac{1}{2 x - 3} \frac{d}{d x} (2 x - 3)

\frac{d}{d x} (2 x - 3) = 2

= \frac{1}{ln ( 10 )} \cdot \frac{1}{2 x - 3} \cdot 2

Vereinfache

\frac{1}{ln ( 10 )} \cdot \frac{1}{2 x - 3} \cdot 2 : \frac{2}{ln ( 10 ) ( 2 x - 3 )}

= \frac{2}{ln ( 10 ) ( 2 x - 3 )}

Graph

Beliebte Beispiele

integral of (x^2+12x-4)/(x^3-4x)

\int \frac{x ^{2} + 12 x - 4}{x ^{3} - 4 x} d x

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integral of (x^2)/(x-10)

\int \frac{x ^{2}}{x - 10} d x

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derivative of (x^3-1/(x-1))

\frac{d}{d x} (\frac{x ^{3} - 1}{x - 1})