derivative of (ln(4x)/x)

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (x e^{1})

\int \frac{2}{x ^{2}} cos (\frac{2}{x}) d x

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