derivative of cos(pi/x)

Lösung

\frac{d}{d x} (cos (\frac{π}{x}))

\frac{π sin ( \frac{π}{x} )}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (cos (\frac{π}{x}))

Wende die Kettenregel an:

- sin (\frac{π}{x}) \frac{d}{d x} (\frac{π}{x})

= - sin (\frac{π}{x}) \frac{d}{d x} (\frac{π}{x})

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

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

Vereinfache

- sin (\frac{π}{x}) (- \frac{π}{x ^{2}}) : \frac{π sin ( \frac{π}{x} )}{x ^{2}}

= \frac{π sin ( \frac{π}{x} )}{x ^{2}}

x \to 0 lim (\frac{cos ( 3 x )}{x})

\frac{d}{d x} (e^{- x} cos (x))

\frac{d y}{d x} = \frac{y ^{2} + 1}{x ^{2} + 1}

p a r i t y y = cos (tan (x))

a re a \frac{4}{x}, 16 x, \frac{1}{16} x