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Beliebt Rechnen >

derivative of (x^3-1/2)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (1) = 0

= \frac{1}{2} (3 x^{2} - 0)

Vereinfache

\frac{1}{2} (3 x^{2} - 0) : \frac{3 x ^{2}}{2}

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

Graph

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