derivative of 2xln(4x^2)

Lösung

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

2 (2 ln (2 x) + 2)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

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