derivative of (ln(cos(2x))/x)

Lösung

\frac{d}{d x} (\frac{ln ( cos ( 2 x ) )}{x})

\frac{- 2 x tan ( 2 x ) - ln ( cos ( 2 x ) )}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( cos ( 2 x ) )}{x})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ln ( cos ( 2 x ) ) ) x - \frac{d x}{d x} ln ( cos ( 2 x ) )}{x ^{2}}

\frac{d}{d x} (ln (cos (2 x))) = - 2 tan (2 x)

\frac{d x}{d x} = 1

= \frac{( - 2 tan ( 2 x ) ) x - 1 \cdot ln ( cos ( 2 x ) )}{x ^{2}}

Vereinfache

= \frac{- 2 x tan ( 2 x ) - ln ( cos ( 2 x ) )}{x ^{2}}

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

\frac{d}{d x} (arcsin (x) + arccos (x))

\int 8 x + 1 d x

\int (e^{t} + 1)^{2} d t

x \to 2 lim (\frac{1}{x + 1})