derivative of (ln(4x)/(ln(2x)))

Lösung

\frac{d}{d x} (\frac{ln ( 4 x )}{ln ( 2 x )})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( 4 x )}{ln ( 2 x )})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ln ( 4 x ) ) ln ( 2 x ) - \frac{d}{d x} ( ln ( 2 x ) ) ln ( 4 x )}{( ln ( 2 x ) ) ^{2}}

\frac{d}{d x} (ln (4 x)) = \frac{1}{x}

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

= \frac{\frac{1}{x} ln ( 2 x ) - \frac{1}{x} ln ( 4 x )}{( ln ( 2 x ) ) ^{2}}

Vereinfache

\frac{\frac{1}{x} ln ( 2 x ) - \frac{1}{x} ln ( 4 x )}{ln ^{2} ( 2 x )} : - \frac{ln ( 2 )}{x ln ^{2} ( 2 x )}

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

\int \frac{4 ln ^{2} ( x ) + 9}{x} d x

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

\int csc^{5} (2 x) d x

\int e^{x t} d x

\frac{d}{d x} ((arcsin (2 x))^{2})