derivative x^2(x^3+5)^3

Lösung

ableitung von

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

2 x (x^{3} + 5)^{3} + 9 x^{4} (x^{3} + 5)^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} ((x^{3} + 5)^{3}) = 9 x^{2} (x^{3} + 5)^{2}

= 2 x (x^{3} + 5)^{3} + 9 x^{2} (x^{3} + 5)^{2} x^{2}

9 x^{2} (x^{3} + 5)^{2} x^{2} = 9 x^{4} (x^{3} + 5)^{2}

= 2 x (x^{3} + 5)^{3} + 9 x^{4} (x^{3} + 5)^{2}

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