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Beliebt Rechnen >

derivative of (x^3+2x^2-4/3)

Lösung

\frac{d}{d x} (\frac{x ^{3} + 2 x ^{2} - 4}{3})

Lösung

x^{2} + \frac{4 x}{3}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{3} + 2 x ^{2} - 4}{3})

Entferne die Konstante:

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

= \frac{1}{3} \frac{d}{d x} (x^{3} + 2 x^{2} - 4)

Wende die Summen-/Differenzregel an:

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

= \frac{1}{3} (\frac{d}{d x} (x^{3}) + \frac{d}{d x} (2 x^{2}) - \frac{d}{d x} (4))

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

\frac{d}{d x} (2 x^{2}) = 4 x

\frac{d}{d x} (4) = 0

= \frac{1}{3} (3 x^{2} + 4 x - 0)

Vereinfache

\frac{1}{3} (3 x^{2} + 4 x - 0) : x^{2} + \frac{4 x}{3}

= x^{2} + \frac{4 x}{3}

Graph

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