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Beliebt Rechnen >

derivative ln(2x)*x^2

Lösung

ableitung von

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

Lösung

x + 2 x ln (2 x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

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

= x + 2 x ln (2 x)

Graph

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