derivative y=x^2(x+3)

Lösung

ableitung von

y = x^{2} (x + 3)

3 x^{2} + 6 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 x (x + 3) + 1 \cdot x^{2} : 3 x^{2} + 6 x

= 3 x^{2} + 6 x