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Beliebt Rechnen >

derivative of 5cot(2/x)

Lösung

\frac{d}{d x} (5 cot (\frac{2}{x}))

Lösung

\frac{10 csc ^{2} ( \frac{2}{x} )}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (5 cot (\frac{2}{x}))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (cot (\frac{2}{x}))

Wende die Kettenregel an:

- csc^{2} (\frac{2}{x}) \frac{d}{d x} (\frac{2}{x})

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

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

= 5 (- csc^{2} (\frac{2}{x}) (- \frac{2}{x ^{2}}))

Vereinfache

5 (- csc^{2} (\frac{2}{x}) (- \frac{2}{x ^{2}})) : \frac{10 csc ^{2} ( \frac{2}{x} )}{x ^{2}}

= \frac{10 csc ^{2} ( \frac{2}{x} )}{x ^{2}}

Graph

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