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Beliebt Rechnen >

derivative of log_{7}(ln(x))

Lösung

\frac{d}{d x} (lo g_{7} (ln (x)))

Lösung

\frac{1}{ln ( 7 ) x ln ( x )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{7} (ln (x)))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( ln ( x ) )}{ln ( 7 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 7 )} \frac{d}{d x} (ln (ln (x)))

Wende die Kettenregel an:

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

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

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

= \frac{1}{ln ( 7 )} \cdot \frac{1}{ln ( x )} \cdot \frac{1}{x}

Vereinfache

\frac{1}{ln ( 7 )} \cdot \frac{1}{ln ( x )} \cdot \frac{1}{x} : \frac{1}{ln ( 7 ) x ln ( x )}

= \frac{1}{ln ( 7 ) x ln ( x )}

Graph

Beliebte Beispiele

integral of e^{arccos(x)}

\int e^{a r c c o s (x)} d x

integral of 2x-1/(x^2)

\int 2 x - \frac{1}{x ^{2}} d x

integral of 2^x+x^2

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

(\partial)/(\partial z)(yz-ln(x+z))

\frac{\partial}{\partial z} (yz - ln (x + z))

limit as x approaches-infinity of 7

x \to - \infty lim (7)