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Beliebt Rechnen >

derivative of (x^2+7(5-x))

Lösung

\frac{d}{d x} ((x^{2} + 7) (5 - x))

Lösung

10 x - 3 x^{2} - 7

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + 7) (5 - x))

Wende die Produktregel an:

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

f = x^{2} + 7, g = 5 - x

= \frac{d}{d x} (x^{2} + 7) (5 - x) + \frac{d}{d x} (5 - x) (x^{2} + 7)

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

\frac{d}{d x} (5 - x) = - 1

= 2 x (5 - x) + (- 1) (x^{2} + 7)

Vereinfache

2 x (5 - x) + (- 1) (x^{2} + 7) : 10 x - 3 x^{2} - 7

= 10 x - 3 x^{2} - 7

Graph

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