derivative of (x-1ln(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x - 1, g = ln (x)

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

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

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

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

Vereinfache

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

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

roo t s a sin (\frac{( π \cdot x )}{b})

\frac{d}{d x} (\frac{64}{x ^{2} + 16})

y \to 2 lim (\frac{y ^{3} - 6 y ^{2} + 12 y - 8}{y ^{4} - 4 y ^{3} + 16 y - 16})

d er i v a t i v e ln (c)

\int \frac{z}{z ^{2} + z - 1} d z