derivative of cos(pi/2+1/x)

Lösung

\frac{d}{d x} (cos (\frac{π}{2} + \frac{1}{x}))

\frac{cos ( \frac{1}{x} )}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (cos (\frac{π}{2} + \frac{1}{x}))

Vereinfache

cos (\frac{π}{2} + \frac{1}{x}) : - sin (\frac{1}{x})

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

t an g e n t \frac{1}{x + 4}

\int (3 x^{2} + 6) d x

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\int_{- 6}^{6} \frac{1}{36 - x ^{2}} d x