derivative y=log_{5}(sqrt(5x+4))

Lösung

ableitung von

y = lo g_{5} (5 x + 4)

\frac{5}{2 ln ( 5 ) ( 5 x + 4 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{5} (5 x + 4))

Wende die log Regel an:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( 5 x + 4 )}{ln ( 5 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (5 x + 4))

Wende die Kettenregel an:

\frac{1}{5 x + 4} \frac{d}{d x} (5 x + 4)

= \frac{1}{5 x + 4} \frac{d}{d x} (5 x + 4)

\frac{d}{d x} (5 x + 4) = \frac{5}{2 5 x + 4}

= \frac{1}{ln ( 5 )} \cdot \frac{1}{5 x + 4} \cdot \frac{5}{2 5 x + 4}

Vereinfache

\frac{1}{ln ( 5 )} \cdot \frac{1}{5 x + 4} \cdot \frac{5}{2 5 x + 4} : \frac{5}{2 ln ( 5 ) ( 5 x + 4 )}

= \frac{5}{2 ln ( 5 ) ( 5 x + 4 )}

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