derivative f(x)=(x-4)(x^2+8)

Lösung

ableitung von

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

3 x^{2} - 8 x + 8

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (x - 4) = 1

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

= 1 \cdot (x^{2} + 8) + 2 x (x - 4)

Vereinfache

1 \cdot (x^{2} + 8) + 2 x (x - 4) : 3 x^{2} - 8 x + 8

= 3 x^{2} - 8 x + 8

y^{^{'}} = 4 y + y^{4}

\frac{d}{d x} (\frac{x ^{2} - 9 x + 14}{( x - 5 ) ( x - 10 )})

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