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Beliebt Rechnen >

derivative of (x^2*ln(x))

Lösung

\frac{d}{d x} ((x^{2}) \cdot ln (x))

Lösung

2 x ln (x) + x

Schritte zur Lösung

\frac{d}{d x} ((x^{2}) ln (x))

Wende die Produktregel an:

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

f = x^{2}, g = ln (x)

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

\frac{1}{x} x^{2} = x

= 2 x ln (x) + x

Graph

Beliebte Beispiele

derivative f(x)=(x^2)/(9+2x)

d er i v a t i v e f (x) = \frac{x ^{2}}{9 + 2 x}

integral from 0 to 1 of pi(x-x^{10})

\int_{0}^{1} π (x - x^{10}) d x

derivative of 3x^2e^x+x^3e^x

\frac{d}{d x} (3 x^{2} e^{x} + x^{3} e^{x})

derivative 4x^3-12x^2

d er i v a t i v e 4 x^{3} - 12 x^{2}

derivative of e^{7x-4}

\frac{d}{d x} (e^{7 x - 4})