derivative of ln(tanh(x/2))

Lösung

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

\frac{sech ^{2} ( \frac{x}{2} )}{2 tanh ( \frac{x}{2} )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{tanh ( \frac{x}{2} )} sech^{2} (\frac{x}{2}) \frac{1}{2}

Vereinfache

\frac{1}{tanh ( \frac{x}{2} )} sech^{2} (\frac{x}{2}) \frac{1}{2} : \frac{sech ^{2} ( \frac{x}{2} )}{2 tanh ( \frac{x}{2} )}

= \frac{sech ^{2} ( \frac{x}{2} )}{2 tanh ( \frac{x}{2} )}

\int 7 (1 + tan^{2} (x)) d x

\frac{d}{d x} (e^{- a x})

\frac{d}{d x} (\frac{3 x ^{2} + 3}{x})

\int \frac{t ^{3}}{4 3 + t ^{4}} d t

\int_{0}^{1} e^{- s t} (t) d t