derivative of arccos(x/pi)

Lösung

\frac{d}{d x} (arccos (\frac{x}{π}))

- \frac{1}{π ^{2} - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (arccos (\frac{x}{π}))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x}{π}) = \frac{1}{π}

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

Vereinfache

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

= - \frac{1}{π ^{2} - x ^{2}}

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