derivative of (ln(3x+1)/(6x+2))

Lösung

\frac{d}{d x} (\frac{ln ( 3 x + 1 )}{6 x + 2})

- \frac{3 ( ln ( 3 x + 1 ) - 1 )}{2 ( 3 x + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( 3 x + 1 )}{6 x + 2})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ln ( 3 x + 1 ) ) ( 6 x + 2 ) - \frac{d}{d x} ( 6 x + 2 ) ln ( 3 x + 1 )}{( 6 x + 2 ) ^{2}}

\frac{d}{d x} (ln (3 x + 1)) = \frac{3}{3 x + 1}

\frac{d}{d x} (6 x + 2) = 6

= \frac{\frac{3}{3 x + 1} ( 6 x + 2 ) - 6 ln ( 3 x + 1 )}{( 6 x + 2 ) ^{2}}

Vereinfache

\frac{\frac{3}{3 x + 1} ( 6 x + 2 ) - 6 ln ( 3 x + 1 )}{( 6 x + 2 ) ^{2}} : - \frac{3 ( ln ( 3 x + 1 ) - 1 )}{2 ( 3 x + 1 ) ^{2}}

= - \frac{3 ( ln ( 3 x + 1 ) - 1 )}{2 ( 3 x + 1 ) ^{2}}