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Beliebt Rechnen >

derivative of (x+1(x^3+3))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x + 1, g = x^{3} + 3

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

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

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

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

Vereinfache

1 \cdot (x^{3} + 3) + 3 x^{2} (x + 1) : 4 x^{3} + 3 x^{2} + 3

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

Graph

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