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Beliebt Rechnen >

derivative f(x)=sqrt(x^2+3x)

Lösung

ableitung von

f (x) = x^{2} + 3 x

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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