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Beliebt Rechnen >

derivative of xln(x+1)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative of 8(x-3^{2/3})

\frac{d}{d x} (8 (x - 3)^{\frac{2}{3}})

integral from 0 to 1 of sqrt(x+9)

\int_{0}^{1} x + 9 d x

(\partial)/(\partial x)(e^{-rx})

\frac{\partial}{\partial x} (e^{- r x})

derivative 3/(sqrt(x+7))

d er i v a t i v e \frac{3}{x + 7}

integral of 0.2x^2+1

\int 0.2 x^{2} + 1 d x