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Beliebt Vorkalkül >

derivative ln(2x-1)-ln(x-1)

Lösung

ableitung von

ln (2 x - 1) - ln (x - 1)

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= \frac{2}{2 x - 1} - \frac{1}{x - 1}

Vereinfache

\frac{2}{2 x - 1} - \frac{1}{x - 1} : - \frac{1}{( x - 1 ) ( 2 x - 1 )}

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

Graph

Beliebte Beispiele

derivative f(x)=sin(2x)

d er i v a t i v e f (x) = sin (2 x)

l in e y = 3 x + 5

normal y=(x^2)/(x-1),(0,0)

n or ma l y = \frac{x ^{2}}{x - 1}, (0, 0)

derivative f(x)=(x^2-3x)ln(x^2-3x)

d er i v a t i v e f (x) = (x^{2} - 3 x) ln (x^{2} - 3 x)

z = - 3 - 3 i