derivative ln(144sin^2(x))

Lösung

ableitung von

ln (144 sin^{2} (x))

2 cot (x)

Schritte zur Lösung

\frac{d}{d x} (ln (144 sin^{2} (x)))

Wende die Kettenregel an:

\frac{1}{144 sin ^{2} ( x )} \frac{d}{d x} (144 sin^{2} (x))

= \frac{1}{144 sin ^{2} ( x )} \frac{d}{d x} (144 sin^{2} (x))

\frac{d}{d x} (144 sin^{2} (x)) = 288 sin (x) cos (x)

= \frac{1}{144 sin ^{2} ( x )} \cdot 288 sin (x) cos (x)

Vereinfache

\frac{1}{144 sin ^{2} ( x )} \cdot 288 sin (x) cos (x) : 2 cot (x)

= 2 cot (x)