derivative of arccsc(x/2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{4 + x}{4 - x})

d er i v a t i v e e^{\frac{1}{x}}

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

x \to 2 lim (\frac{3}{∣ x - 2 ∣})

y d x + (- 2 x - 2 y) d y = 0