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Beliebt Rechnen >

derivative of (x-1ln(x))

Lösung

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

Lösung

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}

Graph

Beliebte Beispiele

wurzeln von asin(((pi*x))/b)

derivative of (64/(x^2+16))

limit as y approaches 2 of (y^3-6y^2+12y-8)/(y^4-4y^3+16y-16)

derivative ln(c)

integral of z/(z^2+z-1)