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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

2 ln (2 x - 1) + 2

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 2 x - 1, g = ln (2 x - 1)

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

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

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

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

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

= 2 ln (2 x - 1) + 2

Graph

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