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Beliebt Rechnen >

derivative arctan(x^4)

Lösung

ableitung von

arctan (x^{4})

Lösung

\frac{4 x ^{3}}{x ^{8} + 1}

Schritte zur Lösung

\frac{d}{d x} (arctan (x^{4}))

Wende die Kettenregel an:

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

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

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

= \frac{1}{( x ^{4} ) ^{2} + 1} \cdot 4 x^{3}

Vereinfache

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

= \frac{4 x ^{3}}{x ^{8} + 1}

Graph

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