derivative of ln((cos(x)/(sin(x))))

Lösung

\frac{d}{d x} (ln (\frac{cos ( x )}{sin ( x )}))

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

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{cos ( x )}{sin ( x )}))

Vereinfache

ln (\frac{cos ( x )}{sin ( x )}) : ln (cot (x))

= \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)

\int cos (a x + b) d x

\int csch^{2} (x) d x

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

\int \frac{x ^{2} - 5 x - 6}{x ^{2} - 4} d x

\frac{\partial}{\partial x} (3 x e^{2 x y})