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

Solución

derivada de

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

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

Pasos de solución

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

Aplicar la regla de la suma/diferencia:

(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}

Simplificar

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

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

f (x) = sin (2 x)

y = 3 x + 5

y = \frac{x ^{2}}{x - 1}, (0, 0)

f (x) = (x^{2} - 3 x) ln (x^{2} - 3 x)

z = - 3 - 3 i