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Beliebt Rechnen >

derivative f(x)=(x^2+1)^3(x^2+2)^6

Lösung

ableitung von

f (x) = (x^{2} + 1)^{3} (x^{2} + 2)^{6}

Lösung

6 x (x^{2} + 1)^{2} (x^{2} + 2)^{6} + 12 x (x^{2} + 2)^{5} (x^{2} + 1)^{3}

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + 1)^{3} (x^{2} + 2)^{6})

Wende die Produktregel an:

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

f = (x^{2} + 1)^{3}, g = (x^{2} + 2)^{6}

= \frac{d}{d x} ((x^{2} + 1)^{3}) (x^{2} + 2)^{6} + \frac{d}{d x} ((x^{2} + 2)^{6}) (x^{2} + 1)^{3}

\frac{d}{d x} ((x^{2} + 1)^{3}) = 6 x (x^{2} + 1)^{2}

\frac{d}{d x} ((x^{2} + 2)^{6}) = 12 x (x^{2} + 2)^{5}

= 6 x (x^{2} + 1)^{2} (x^{2} + 2)^{6} + 12 x (x^{2} + 2)^{5} (x^{2} + 1)^{3}

Graph

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