derivative ln(tan(x/2))

Lösung

ableitung von

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)

d er i v a t i v e 4 e^{2} x

d er i v a t i v e \frac{( x ^{2} )}{10}

\frac{d}{d q} ((1 + sec (q)) sin (q))

\frac{d}{d r} (\frac{g \cdot ( m _{1} \cdot m _{2} )}{( r ^{2} )})

\frac{d}{d a} (2 sin^{2} (a) cos^{2} (a))