derivative of 1/(2sin(x))

Lösung

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

- \frac{cot ( x )}{2 sin ( x )}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (sin (x)) = cos (x)

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

Vereinfache

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

= - \frac{cot ( x )}{2 sin ( x )}

t an g e n t 2 sin (x)

\frac{\partial}{\partial m} (- m g (m) sin (a))

x \to 3 lim (\frac{27 - x}{x - 3})

\int_{0}^{π} π (sin^{2} (x)) d x

x \to 5 - lim (x)