derivative of ln(tan(x/2))

Lösung

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

csc (x)

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{tan ( \frac{x}{2} )} sec^{2} (\frac{x}{2}) \frac{1}{2}

Vereinfache

\frac{1}{tan ( \frac{x}{2} )} sec^{2} (\frac{x}{2}) \frac{1}{2} : csc (x)

= csc (x)

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

in v erse l a pl a ce \frac{e ^{- 5 s}}{s + 1}

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

y^{^{''}} + 4 y = sin^{2} (x)

\int 3 tan (4 x) sec^{2} (4 x) d x