derivative arccos(4x^9)

Lösung

ableitung von

arccos (4 x^{9})

- \frac{36 x ^{8}}{1 - 16 x ^{18}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (4 x^{9}) = 36 x^{8}

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

Vereinfache

- \frac{1}{1 - ( 4 x ^{9} ) ^{2}} \cdot 36 x^{8} : - \frac{36 x ^{8}}{1 - 16 x ^{18}}

= - \frac{36 x ^{8}}{1 - 16 x ^{18}}

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