derivative y=(ln(6x))/(6x)

Lösung

ableitung von

y = \frac{ln ( 6 x )}{6 x}

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

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( 6 x )}{6 x})

Entferne die Konstante:

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

= \frac{1}{6} \frac{d}{d x} (\frac{ln ( 6 x )}{x})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (ln (6 x)) = \frac{1}{x}

\frac{d x}{d x} = 1

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

Vereinfache

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

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

\frac{d ^{2}}{d x ^{2}} (11 x)

n = 1 \sum \infty \frac{6}{n ( n + 2 )}

\int_{0}^{1} (x^{2} + 2) e^{- x} d x

\frac{d y}{d x} = 9 y e^{x + 5}

y^{^{'}} = x sin (2 y)