derivative of ln(cos((x-1/x)))

Lösung

\frac{d}{d x} (ln (cos (\frac{x - 1}{x})))

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

Schritte zur Lösung

\frac{d}{d x} (ln (cos (\frac{x - 1}{x})))

Wende die Kettenregel an:

\frac{1}{cos ( \frac{x - 1}{x} )} \frac{d}{d x} (cos (\frac{x - 1}{x}))

= \frac{1}{cos ( \frac{x - 1}{x} )} \frac{d}{d x} (cos (\frac{x - 1}{x}))

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

= \frac{1}{cos ( \frac{x - 1}{x} )} (- \frac{sin ( \frac{x - 1}{x} )}{x ^{2}})

Vereinfache

\frac{1}{cos ( \frac{x - 1}{x} )} (- \frac{sin ( \frac{x - 1}{x} )}{x ^{2}}) : - \frac{tan ( \frac{x - 1}{x} )}{x ^{2}}

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

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

\int_{1}^{2} \frac{x}{x ^{2} + 4 x + 20} d x

\int_{0}^{0.4} \frac{( x ^{2} )}{4 - 25 x ^{2}} d x

\frac{\partial}{\partial x} (y x - y - x)

y^{^{'}} = 5 x - y