derivative f(x)=(x^3-4)^2(2x+5)^3

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

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