derivative of xln(5x)

Lösung

\frac{d}{d x} (x ln (5 x))

ln (5 x) + 1

Schritte zur Lösung

\frac{d}{d x} (x ln (5 x))

Wende die Produktregel an:

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

f = x, g = ln (5 x)

= \frac{d x}{d x} ln (5 x) + \frac{d}{d x} (ln (5 x)) x

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

\frac{d}{d x} (ln (5 x)) = \frac{1}{x}

= 1 \cdot ln (5 x) + \frac{1}{x} x

Vereinfache

1 \cdot ln (5 x) + \frac{1}{x} x : ln (5 x) + 1

= ln (5 x) + 1