derivative of (arccos(x)/x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

Vereinfache

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

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

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