derivative of sqrt(2x^4-2x)

Lösung

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

\frac{4 x ^{3} - 1}{2 x ^{4} - 2 x}

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{2 2 x ^{4} - 2 x} \frac{d}{d x} (2 x^{4} - 2 x)

= \frac{1}{2 2 x ^{4} - 2 x} \frac{d}{d x} (2 x^{4} - 2 x)

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

= \frac{1}{2 2 x ^{4} - 2 x} (8 x^{3} - 2)

Vereinfache

\frac{1}{2 2 x ^{4} - 2 x} (8 x^{3} - 2) : \frac{4 x ^{3} - 1}{2 x ^{4} - 2 x}

= \frac{4 x ^{3} - 1}{2 x ^{4} - 2 x}

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