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Beliebt Rechnen >

derivative of xln(x^{18})

Lösung

\frac{d}{d x} (x ln (x^{18}))

Lösung

18 ln (x) + 18

Schritte zur Lösung

\frac{d}{d x} (x ln (x^{18}))

Wende die Produktregel an:

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

f = x, g = ln (x^{18})

= \frac{d x}{d x} ln (x^{18}) + \frac{d}{d x} (ln (x^{18})) x

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

\frac{d}{d x} (ln (x^{18})) = \frac{18}{x}

= 1 \cdot ln (x^{18}) + \frac{18}{x} x

Vereinfache

1 \cdot ln (x^{18}) + \frac{18}{x} x : 18 ln (x) + 18

= 18 ln (x) + 18

Graph

Beliebte Beispiele

integral of (x^2+3x-1)/(x+2)

\int \frac{x ^{2} + 3 x - 1}{x + 2} d x

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\int_{0}^{3} (8 - 2 x) d x

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integral of e^{-3/2 x}

\int e^{- \frac{3}{2} x} d x

fläche 7cos(pix),8x^2-2,[-0.5,0.5]

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