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Beliebt Rechnen >

derivative of sqrt(x^2+x+3)

Lösung

\frac{d}{d x} (x^{2} + x + 3)

Lösung

\frac{2 x + 1}{2 x ^{2} + x + 3}

Schritte zur Lösung

\frac{d}{d x} (x^{2} + x + 3)

Wende die Kettenregel an:

\frac{1}{2 x ^{2} + x + 3} \frac{d}{d x} (x^{2} + x + 3)

= \frac{1}{2 x ^{2} + x + 3} \frac{d}{d x} (x^{2} + x + 3)

\frac{d}{d x} (x^{2} + x + 3) = 2 x + 1

= \frac{1}{2 x ^{2} + x + 3} (2 x + 1)

Vereinfache

\frac{1}{2 x ^{2} + x + 3} (2 x + 1) : \frac{2 x + 1}{2 x ^{2} + x + 3}

= \frac{2 x + 1}{2 x ^{2} + x + 3}

Graph

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