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Beliebt Rechnen >

derivative g(x)=sqrt(x+x^3)

Lösung

ableitung von

g (x) = x + x^{3}

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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