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Beliebt Rechnen >

derivative f(x)=sqrt(2x^2+1)

Lösung

ableitung von

f (x) = 2 x^{2} + 1

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (2 x^{2} + 1) = 4 x

= \frac{1}{2 2 x ^{2} + 1} \cdot 4 x

Vereinfache

\frac{1}{2 2 x ^{2} + 1} \cdot 4 x : \frac{2 x}{2 x ^{2} + 1}

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

Graph

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