(\partial)/(\partial x)(-ln(x^2+1))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- \frac{1}{x ^{2} + 1} \cdot 2 x : - \frac{2 x}{x ^{2} + 1}

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