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Beliebt Rechnen >

derivative sqrt(x^2+6x+9)

Lösung

ableitung von

x^{2} + 6 x + 9

Lösung

\frac{x + 3}{x ^{2} + 6 x + 9}

Schritte zur Lösung

\frac{d}{d x} (x^{2} + 6 x + 9)

Wende die Kettenregel an:

\frac{1}{2 x ^{2} + 6 x + 9} \frac{d}{d x} (x^{2} + 6 x + 9)

= \frac{1}{2 x ^{2} + 6 x + 9} \frac{d}{d x} (x^{2} + 6 x + 9)

\frac{d}{d x} (x^{2} + 6 x + 9) = 2 x + 6

= \frac{1}{2 x ^{2} + 6 x + 9} (2 x + 6)

Vereinfache

\frac{1}{2 x ^{2} + 6 x + 9} (2 x + 6) : \frac{x + 3}{x ^{2} + 6 x + 9}

= \frac{x + 3}{x ^{2} + 6 x + 9}

Graph

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