(\partial)/(\partial x)(arcsin(-2x^4))

Lösung

\frac{\partial}{\partial x} (arcsin (- 2 x^{4}))

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

Schritte zur Lösung

\frac{\partial}{\partial x} (arcsin (- 2 x^{4}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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