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Beliebt Rechnen >

derivative of arcsin(2x^5)

Lösung

\frac{d}{d x} (arcsin (2 x^{5}))

Lösung

\frac{10 x ^{4}}{1 - 4 x ^{10}}

Schritte zur Lösung

\frac{d}{d x} (arcsin (2 x^{5}))

Wende die Kettenregel an:

\frac{1}{1 - ( 2 x ^{5} ) ^{2}} \frac{d}{d x} (2 x^{5})

= \frac{1}{1 - ( 2 x ^{5} ) ^{2}} \frac{d}{d x} (2 x^{5})

\frac{d}{d x} (2 x^{5}) = 10 x^{4}

= \frac{1}{1 - ( 2 x ^{5} ) ^{2}} \cdot 10 x^{4}

Vereinfache

\frac{1}{1 - ( 2 x ^{5} ) ^{2}} \cdot 10 x^{4} : \frac{10 x ^{4}}{1 - 4 x ^{10}}

= \frac{10 x ^{4}}{1 - 4 x ^{10}}

Graph

Beliebte Beispiele

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