derivative of ln(x^2+2x)

Lösung

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

\frac{2 x + 2}{x ^{2} + 2 x}

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{x ^{2} + 2 x} \frac{d}{d x} (x^{2} + 2 x)

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

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

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

Vereinfache

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

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

x \to 0 lim (ln (2 x^{2} + x))

\int \frac{x}{x ^{2} + 49} d x

in v erse l a pl a ce \frac{1}{( s - 3 ) ( s - 9 )}

(x, y) \to (0, 0) lim (\frac{( sin ( 2 x ) - 2 x + y )}{x ^{3} + y})

\int ln (x) \cdot ln (x) d x