(\partial)/(\partial x)(ln(x^2+x))

Lösung

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

\frac{2 x + 1}{x ^{2} + x}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (4 x - 4 - y^{2})

d er i v a t i v e \frac{85 t}{99 t - 85}

x \to 3 lim (x^{2} + 2 x - 1)

v + x \cdot \frac{d v}{d x} = x^{2} - 1 + 2 v

d er i v a t i v e b cos (x) + x^{2} sin (x)