derivative of arcsin(9x^4)

Lösung

\frac{d}{d x} (arcsin (9 x^{4}))

\frac{36 x ^{3}}{1 - 81 x ^{8}}

Schritte zur Lösung

\frac{d}{d x} (arcsin (9 x^{4}))

Wende die Kettenregel an:

\frac{1}{1 - ( 9 x ^{4} ) ^{2}} \frac{d}{d x} (9 x^{4})

= \frac{1}{1 - ( 9 x ^{4} ) ^{2}} \frac{d}{d x} (9 x^{4})

\frac{d}{d x} (9 x^{4}) = 36 x^{3}

= \frac{1}{1 - ( 9 x ^{4} ) ^{2}} \cdot 36 x^{3}

Vereinfache

\frac{1}{1 - ( 9 x ^{4} ) ^{2}} \cdot 36 x^{3} : \frac{36 x ^{3}}{1 - 81 x ^{8}}

= \frac{36 x ^{3}}{1 - 81 x ^{8}}

\frac{d}{d y} (\frac{6 x + y}{8 z - 5 y})

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