((ln(x))/x)^'

Lösung

(\frac{ln ( x )}{x})^{^{'}}

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

Schritte zur Lösung

(\frac{ln ( x )}{x})^{'}

Wende die Quotientenregel an:

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

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

(ln (x))^{'} = \frac{1}{x}

x^{'} = 1

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

Vereinfache

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

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

x \to + 4 lim (x - 2)

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