derivative of (x^3-7(2x^2+3))

Lösung

\frac{d}{d x} ((x^{3} - 7) (2 x^{2} + 3))

10 x^{4} + 9 x^{2} - 28 x

Schritte zur Lösung

\frac{d}{d x} ((x^{3} - 7) (2 x^{2} + 3))

Wende die Produktregel an:

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

f = x^{3} - 7, g = 2 x^{2} + 3

= \frac{d}{d x} (x^{3} - 7) (2 x^{2} + 3) + \frac{d}{d x} (2 x^{2} + 3) (x^{3} - 7)

\frac{d}{d x} (x^{3} - 7) = 3 x^{2}

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

= 3 x^{2} (2 x^{2} + 3) + 4 x (x^{3} - 7)

Vereinfache

3 x^{2} (2 x^{2} + 3) + 4 x (x^{3} - 7) : 10 x^{4} + 9 x^{2} - 28 x

= 10 x^{4} + 9 x^{2} - 28 x

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