derivative (x^4-3)^3(x^2+6)^5

Lösung

ableitung von

(x^{4} - 3)^{3} (x^{2} + 6)^{5}

12 x^{3} (x^{4} - 3)^{2} (x^{2} + 6)^{5} + 10 x (x^{2} + 6)^{4} (x^{4} - 3)^{3}

Schritte zur Lösung

\frac{d}{d x} ((x^{4} - 3)^{3} (x^{2} + 6)^{5})

Wende die Produktregel an:

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

f = (x^{4} - 3)^{3}, g = (x^{2} + 6)^{5}

= \frac{d}{d x} ((x^{4} - 3)^{3}) (x^{2} + 6)^{5} + \frac{d}{d x} ((x^{2} + 6)^{5}) (x^{4} - 3)^{3}

\frac{d}{d x} ((x^{4} - 3)^{3}) = 12 x^{3} (x^{4} - 3)^{2}

\frac{d}{d x} ((x^{2} + 6)^{5}) = 10 x (x^{2} + 6)^{4}

= 12 x^{3} (x^{4} - 3)^{2} (x^{2} + 6)^{5} + 10 x (x^{2} + 6)^{4} (x^{4} - 3)^{3}

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