derivative of ln(cot(x))

Lösung

\frac{d}{d x} (ln (cot (x)))

- csc^{2} (x) tan (x)

Schritte zur Lösung

\frac{d}{d x} (ln (cot (x)))

Wende die Kettenregel an:

\frac{1}{cot ( x )} \frac{d}{d x} (cot (x))

= \frac{1}{cot ( x )} \frac{d}{d x} (cot (x))

\frac{d}{d x} (cot (x)) = - csc^{2} (x)

= \frac{1}{cot ( x )} (- csc^{2} (x))

Vereinfache

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

= - csc^{2} (x) tan (x)

x \to - 5 - lim (x^{2} + \frac{4}{x + 5})

x \to 2 lim (\frac{x ^{4} - 9}{x + 2})

\frac{d}{d x} (- \frac{10 x}{( x ^{2} - 4 ) ^{2}})

t an g e n t f (x) = \frac{1}{x + 8}, at x = 9

n = 2 \sum \infty \frac{1}{n ^{3}}