derivative of arcsin(x/6)

Lösung

\frac{d}{d x} (arcsin (\frac{x}{6}))

\frac{1}{36 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (arcsin (\frac{x}{6}))

Wende die Kettenregel an:

\frac{1}{1 - ( \frac{x}{6} ) ^{2}} \frac{d}{d x} (\frac{x}{6})

= \frac{1}{1 - ( \frac{x}{6} ) ^{2}} \frac{d}{d x} (\frac{x}{6})

\frac{d}{d x} (\frac{x}{6}) = \frac{1}{6}

= \frac{1}{1 - ( \frac{x}{6} ) ^{2}} \cdot \frac{1}{6}

Vereinfache

\frac{1}{1 - ( \frac{x}{6} ) ^{2}} \cdot \frac{1}{6} : \frac{1}{36 - x ^{2}}

= \frac{1}{36 - x ^{2}}

\frac{d}{d x} (e^{x y})

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