derivative arcsin(1/x)

Lösung

ableitung von

arcsin (\frac{1}{x})

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

Schritte zur Lösung

\frac{d}{d x} (arcsin (\frac{1}{x}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (ln (x^{2} + 1) + y^{2} - z)

\frac{\partial}{\partial x} (e^{z} (x - y)^{2})

a re a x^{2} - 4, y = 0

\int 64 x^{2} cos (4 x) d x

d er i v a t i v e g (t) = \frac{9}{t}