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Beliebt Rechnen >

derivative of (x^4+2^2(x^5+4)^4)

Lösung

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

Lösung

8 x^{3} (x^{4} + 2) (x^{5} + 4)^{4} + 20 x^{4} (x^{5} + 4)^{3} (x^{4} + 2)^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} ((x^{4} + 2)^{2}) = 8 x^{3} (x^{4} + 2)

\frac{d}{d x} ((x^{5} + 4)^{4}) = 20 x^{4} (x^{5} + 4)^{3}

= 8 x^{3} (x^{4} + 2) (x^{5} + 4)^{4} + 20 x^{4} (x^{5} + 4)^{3} (x^{4} + 2)^{2}

Graph

Beliebte Beispiele

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\int (x^{4} - (- 3)) d x

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\int 3 e^{7} d x