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Beliebt Rechnen >

derivative f(x)=xsqrt(x^3-6)

Lösung

ableitung von

f (x) = x x^{3} - 6

Lösung

\frac{5 x ^{3} - 12}{2 x ^{3} - 6}

Schritte zur Lösung

\frac{d}{d x} (x x^{3} - 6)

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{3} - 6

= \frac{d x}{d x} x^{3} - 6 + \frac{d}{d x} (x^{3} - 6) x

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{3} - 6) = \frac{3 x ^{2}}{2 x ^{3} - 6}

= 1 \cdot x^{3} - 6 + \frac{3 x ^{2}}{2 x ^{3} - 6} x

Vereinfache

1 \cdot x^{3} - 6 + \frac{3 x ^{2}}{2 x ^{3} - 6} x : \frac{5 x ^{3} - 12}{2 x ^{3} - 6}

= \frac{5 x ^{3} - 12}{2 x ^{3} - 6}

Graph

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