derivative of ln(sin(x/2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int (3^{5 x - 2}) d x

\int_{- 1}^{3} 3 x e^{2 x^{2} - 5} d x

x \to 1 lim (\frac{3 x + 7 - 2}{x ^{3} - 1})

\int x + x d x

x \to 0 lim (\frac{x - 5}{x - 1})