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Beliebt Rechnen >

derivative (4x^2+5)(4x-3)

Lösung

ableitung von

(4 x^{2} + 5) (4 x - 3)

Lösung

48 x^{2} - 24 x + 20

Schritte zur Lösung

\frac{d}{d x} ((4 x^{2} + 5) (4 x - 3))

Wende die Produktregel an:

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

f = 4 x^{2} + 5, g = 4 x - 3

= \frac{d}{d x} (4 x^{2} + 5) (4 x - 3) + \frac{d}{d x} (4 x - 3) (4 x^{2} + 5)

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

\frac{d}{d x} (4 x - 3) = 4

= 8 x (4 x - 3) + 4 (4 x^{2} + 5)

Vereinfache

8 x (4 x - 3) + 4 (4 x^{2} + 5) : 48 x^{2} - 24 x + 20

= 48 x^{2} - 24 x + 20

Graph

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