derivative log_{10}(x-1)

Lösung

ableitung von

lo g_{10} (x - 1)

\frac{1}{ln ( 10 ) ( x - 1 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{10} (x - 1))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( x - 1 )}{ln ( 10 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (x - 1))

Wende die Kettenregel an:

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

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

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

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x - 1} \cdot 1

Vereinfache

\frac{1}{ln ( 10 )} \cdot \frac{1}{x - 1} \cdot 1 : \frac{1}{ln ( 10 ) ( x - 1 )}

= \frac{1}{ln ( 10 ) ( x - 1 )}

\frac{d}{d s} (3 s^{2})

d er i v a t i v e y = \frac{( x ^{5} + x ^{2} )}{( x ^{3} + 1 )}

\frac{d}{d t} (65 + 2 t - 3 t^{2})

d er i v a t i v e - 2 ln (x)

d er i v a t i v e f (x) = (x + sin (x))^{2}