derivative (8(2x)^4+5)^3

Lösung

ableitung von

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

1536 x^{3} (128 x^{4} + 5)^{2}

Schritte zur Lösung

\frac{d}{d x} ((8 (2 x)^{4} + 5)^{3})

Vereinfache

(8 (2 x)^{4} + 5)^{3} : (128 x^{4} + 5)^{3}

= \frac{d}{d x} ((128 x^{4} + 5)^{3})

Wende die Kettenregel an:

3 (128 x^{4} + 5)^{2} \frac{d}{d x} (128 x^{4} + 5)

= 3 (128 x^{4} + 5)^{2} \frac{d}{d x} (128 x^{4} + 5)

\frac{d}{d x} (128 x^{4} + 5) = 512 x^{3}

= 3 (128 x^{4} + 5)^{2} \cdot 512 x^{3}

Vereinfache

= 1536 x^{3} (128 x^{4} + 5)^{2}

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