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Beliebt Rechnen >

derivative f(x)=(x-5)^6(x+3)^2

Lösung

ableitung von

f (x) = (x - 5)^{6} (x + 3)^{2}

Lösung

6 (x - 5)^{5} (x + 3)^{2} + 2 (x + 3) (x - 5)^{6}

Schritte zur Lösung

\frac{d}{d x} ((x - 5)^{6} (x + 3)^{2})

Wende die Produktregel an:

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

f = (x - 5)^{6}, g = (x + 3)^{2}

= \frac{d}{d x} ((x - 5)^{6}) (x + 3)^{2} + \frac{d}{d x} ((x + 3)^{2}) (x - 5)^{6}

\frac{d}{d x} ((x - 5)^{6}) = 6 (x - 5)^{5}

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

= 6 (x - 5)^{5} (x + 3)^{2} + 2 (x + 3) (x - 5)^{6}

Graph

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