derivative of arcsin(2/x)

Lösung

\frac{d}{d x} (arcsin (\frac{2}{x}))

- \frac{2}{x x ^{2} - 4}

Schritte zur Lösung

\frac{d}{d x} (arcsin (\frac{2}{x}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{2}{x x ^{2} - 4}

(x^{2} + y + y^{2}) d x - x d y = 0

\int \frac{7}{x ^{2} + 3 x - 10} d x

n = 2 \sum \infty \frac{1}{n}

\int_{0}^{\infty} \frac{8}{x ^{2} + 1} d x

d er i v a t i v e sec^{2} (4 x)