derivative of log_{3}(5x-1)

Lösung

\frac{d}{d x} (lo g_{3} (5 x - 1))

\frac{5}{ln ( 3 ) ( 5 x - 1 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{3} (5 x - 1))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( 5 x - 1 )}{ln ( 3 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (5 x - 1))

Wende die Kettenregel an:

\frac{1}{5 x - 1} \frac{d}{d x} (5 x - 1)

= \frac{1}{5 x - 1} \frac{d}{d x} (5 x - 1)

\frac{d}{d x} (5 x - 1) = 5

= \frac{1}{ln ( 3 )} \cdot \frac{1}{5 x - 1} \cdot 5

Vereinfache

\frac{1}{ln ( 3 )} \cdot \frac{1}{5 x - 1} \cdot 5 : \frac{5}{ln ( 3 ) ( 5 x - 1 )}

= \frac{5}{ln ( 3 ) ( 5 x - 1 )}

d er i v a t i v e \frac{1}{2 r} + \frac{1}{9 r ^{\frac{8}{9}}}

\int - 9.8 d x

\frac{\partial}{\partial x} (11 x^{2} y + 8 x y^{3})

\frac{d}{d x} (\frac{1}{( 4 x ) ^{3}})

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