derivative f(x)=(x^2-10x)*(x-14)

Lösung

ableitung von

f (x) = (x^{2} - 10 x) \cdot (x - 14)

3 x^{2} - 48 x + 140

Schritte zur Lösung

\frac{d}{d x} ((x^{2} - 10 x) (x - 14))

Wende die Produktregel an:

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

f = x^{2} - 10 x, g = x - 14

= \frac{d}{d x} (x^{2} - 10 x) (x - 14) + \frac{d}{d x} (x - 14) (x^{2} - 10 x)

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

\frac{d}{d x} (x - 14) = 1

= (2 x - 10) (x - 14) + 1 \cdot (x^{2} - 10 x)

Vereinfache

(2 x - 10) (x - 14) + 1 \cdot (x^{2} - 10 x) : 3 x^{2} - 48 x + 140

= 3 x^{2} - 48 x + 140

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