derivative f(x)=72x^3(3x^4+7)^5

Lösung

ableitung von

f (x) = 72 x^{3} (3 x^{4} + 7)^{5}

72 (3 x^{2} (3 x^{4} + 7)^{5} + 60 x^{6} (3 x^{4} + 7)^{4})

Schritte zur Lösung

\frac{d}{d x} (72 x^{3} (3 x^{4} + 7)^{5})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 72 \frac{d}{d x} (x^{3} (3 x^{4} + 7)^{5})

Wende die Produktregel an:

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

f = x^{3}, g = (3 x^{4} + 7)^{5}

= 72 (\frac{d}{d x} (x^{3}) (3 x^{4} + 7)^{5} + \frac{d}{d x} ((3 x^{4} + 7)^{5}) x^{3})

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

\frac{d}{d x} ((3 x^{4} + 7)^{5}) = 60 x^{3} (3 x^{4} + 7)^{4}

= 72 (3 x^{2} (3 x^{4} + 7)^{5} + 60 x^{3} (3 x^{4} + 7)^{4} x^{3})

60 x^{3} (3 x^{4} + 7)^{4} x^{3} = 60 x^{6} (3 x^{4} + 7)^{4}

= 72 (3 x^{2} (3 x^{4} + 7)^{5} + 60 x^{6} (3 x^{4} + 7)^{4})

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