derivative arcsin(x/4)

Lösung

ableitung von

arcsin (\frac{x}{4})

\frac{1}{16 - x ^{2}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x}{4}) = \frac{1}{4}

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

Vereinfache

\frac{1}{1 - ( \frac{x}{4} ) ^{2}} \cdot \frac{1}{4} : \frac{1}{16 - x ^{2}}

= \frac{1}{16 - x ^{2}}

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