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Beliebt Rechnen >

derivative of (10x-2x^2(16-2x))

Lösung

\frac{d}{d x} ((10 x - 2 x^{2}) (16 - 2 x))

Lösung

12 x^{2} - 104 x + 160

Schritte zur Lösung

\frac{d}{d x} ((10 x - 2 x^{2}) (16 - 2 x))

Wende die Produktregel an:

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

f = 10 x - 2 x^{2}, g = 16 - 2 x

= \frac{d}{d x} (10 x - 2 x^{2}) (16 - 2 x) + \frac{d}{d x} (16 - 2 x) (10 x - 2 x^{2})

\frac{d}{d x} (10 x - 2 x^{2}) = 10 - 4 x

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

= (10 - 4 x) (16 - 2 x) + (- 2) (10 x - 2 x^{2})

Vereinfache

(10 - 4 x) (16 - 2 x) + (- 2) (10 x - 2 x^{2}) : 12 x^{2} - 104 x + 160

= 12 x^{2} - 104 x + 160

Graph

Beliebte Beispiele

y^{^{'}} + 2 x y^{2} = 0

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