d/(dt)(ln(cos(pi/2-t/2)))

Lösung

\frac{d}{d t} (ln (cos (\frac{π}{2} - \frac{t}{2})))

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

Schritte zur Lösung

\frac{d}{d t} (ln (cos (\frac{π}{2} - \frac{t}{2})))

Vereinfache

ln (cos (\frac{π}{2} - \frac{t}{2})) : ln (sin (\frac{t}{2}))

= \frac{d}{d t} (ln (sin (\frac{t}{2})))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int (x + 2) e^{4 - 3 x} d x

n = 1 \sum \infty \frac{3 ^{n}}{n}

l a pl a ce t r an s f or m (t - 1) cos (4 (t - 1))

(x - 1) y^{^{'}} + x y = 6 e^{x}

n = 1 \sum \infty \frac{n !}{n ^{n}}