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Beliebt Rechnen >

(\partial)/(\partial x)(sqrt(x^2+1))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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