derivative of (arccos(x)^{10})

Lösung

\frac{d}{d x} ((arccos (x))^{10})

- \frac{10 arccos ^{9} ( x )}{1 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} ((arccos (x))^{10})

Wende die Kettenregel an:

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

= 10 (arccos (x))^{9} \frac{d}{d x} (arccos (x))

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

= 10 (arccos (x))^{9} (- \frac{1}{1 - x ^{2}})

Vereinfache

10 arccos^{9} (x) (- \frac{1}{1 - x ^{2}}) : - \frac{10 arccos ^{9} ( x )}{1 - x ^{2}}

= - \frac{10 arccos ^{9} ( x )}{1 - x ^{2}}

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

\frac{d}{d x} (sin (x^{3}) + sin^{3} (x))

\frac{d}{d x} ((arctan (x))^{3})

\frac{\partial}{\partial x} (\frac{1}{f ( x )} - \frac{1}{x})

\frac{d}{d x} (y^{2} + x^{2})