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Beliebt Rechnen >

derivative (3sqrt(x)+4)x^2

Lösung

ableitung von

(3 x + 4) x^{2}

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 3 x + 4, g = x^{2}

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

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

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

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

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

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

Graph

Beliebte Beispiele

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

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