derivative of ln(x*x)

Lösung

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

1 + ln (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = ln (x), g = x

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

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

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

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

Vereinfache

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

= 1 + ln (x)

d er i v a t i v e x (x - 2)^{3}

d er i v a t i v e f (x) = \frac{x}{3 + x}

\int_{0}^{π} cos (x) cos (n x) d x

(x^{3} + e^{y}) \frac{d y}{d x} = 3 x^{2}

x \to \infty lim (x - 1)