derivative of x(ln(5x)^2)

Lösung

\frac{d}{d x} (x (ln (5 x))^{2})

ln^{2} (5 x) + 2 ln (5 x)

Schritte zur Lösung

\frac{d}{d x} (x (ln (5 x))^{2})

Wende die Produktregel an:

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

f = x, g = (ln (5 x))^{2}

= \frac{d x}{d x} (ln (5 x))^{2} + \frac{d}{d x} ((ln (5 x))^{2}) x

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

\frac{d}{d x} ((ln (5 x))^{2}) = \frac{2 ln ( 5 x )}{x}

= 1 \cdot (ln (5 x))^{2} + \frac{2 ln ( 5 x )}{x} x

Vereinfache

1 \cdot ln^{2} (5 x) + \frac{2 ln ( 5 x )}{x} x : ln^{2} (5 x) + 2 ln (5 x)

= ln^{2} (5 x) + 2 ln (5 x)

y^{^{'}} - 3 y = e^{3 x} 4 - x^{2}

x \to - 2 - lim (x + 1)

x \to 0 lim (\frac{1}{sin ( 2 x )})

x \to 3 π lim (x^{3} sin^{4} (x))

x \to 0 lim (\frac{3 x ^{2} - 6 x}{x})