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Beliebt Rechnen >

derivative f(x)=2log_{5}(x)

Lösung

ableitung von

f (x) = 2 lo g_{5} (x)

Lösung

\frac{2}{ln ( 5 ) x}

Schritte zur Lösung

\frac{d}{d x} (2 lo g_{5} (x))

Entferne die Konstante:

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

= 2 \frac{d}{d x} (lo g_{5} (x))

Wende die Derivat-Log-Regel an:

\frac{d}{d x} (lo g_{a} (x)) = \frac{1}{x ln ( a )}

= 2 \cdot \frac{1}{x ln ( 5 )}

Vereinfache

2 \cdot \frac{1}{x ln ( 5 )} : \frac{2}{ln ( 5 ) x}

= \frac{2}{ln ( 5 ) x}

Graph

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