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Beliebt Rechnen >

derivative arccsc(x^4+1)

Lösung

ableitung von

arccsc (x^{4} + 1)

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

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