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Beliebt Rechnen >

derivative 4x^2ln(4x)

Lösung

ableitung von

4 x^{2} ln (4 x)

Lösung

4 (2 x ln (4 x) + x)

Schritte zur Lösung

\frac{d}{d x} (4 x^{2} ln (4 x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (x^{2} ln (4 x))

Wende die Produktregel an:

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

f = x^{2}, g = ln (4 x)

= 4 (\frac{d}{d x} (x^{2}) ln (4 x) + \frac{d}{d x} (ln (4 x)) x^{2})

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

\frac{d}{d x} (ln (4 x)) = \frac{1}{x}

= 4 (2 x ln (4 x) + \frac{1}{x} x^{2})

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

= 4 (2 x ln (4 x) + x)

Graph

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