derivative of (8x^2-5x(13x^2+4))

Lösung

\frac{d}{d x} ((8 x^{2} - 5 x) (13 x^{2} + 4))

416 x^{3} - 195 x^{2} + 64 x - 20

Schritte zur Lösung

\frac{d}{d x} ((8 x^{2} - 5 x) (13 x^{2} + 4))

Wende die Produktregel an:

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

f = 8 x^{2} - 5 x, g = 13 x^{2} + 4

= \frac{d}{d x} (8 x^{2} - 5 x) (13 x^{2} + 4) + \frac{d}{d x} (13 x^{2} + 4) (8 x^{2} - 5 x)

\frac{d}{d x} (8 x^{2} - 5 x) = 16 x - 5

\frac{d}{d x} (13 x^{2} + 4) = 26 x

= (16 x - 5) (13 x^{2} + 4) + 26 x (8 x^{2} - 5 x)

Vereinfache

(16 x - 5) (13 x^{2} + 4) + 26 x (8 x^{2} - 5 x) : 416 x^{3} - 195 x^{2} + 64 x - 20

= 416 x^{3} - 195 x^{2} + 64 x - 20

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