derivative of-3csc(x^{2/3})

Lösung

\frac{d}{d x} (- 3 csc (x^{\frac{2}{3}}))

\frac{2 cot ( x ^{\frac{2}{3}} ) csc ( x ^{\frac{2}{3}} )}{x ^{\frac{1}{3}}}

Schritte zur Lösung

\frac{d}{d x} (- 3 csc (x^{\frac{2}{3}}))

Entferne die Konstante:

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

= - 3 \frac{d}{d x} (csc (x^{\frac{2}{3}}))

Wende die Kettenregel an:

- cot (x^{\frac{2}{3}}) csc (x^{\frac{2}{3}}) \frac{d}{d x} (x^{\frac{2}{3}})

= - cot (x^{\frac{2}{3}}) csc (x^{\frac{2}{3}}) \frac{d}{d x} (x^{\frac{2}{3}})

\frac{d}{d x} (x^{\frac{2}{3}}) = \frac{2}{3 x ^{\frac{1}{3}}}

= - 3 (- cot (x^{\frac{2}{3}}) csc (x^{\frac{2}{3}}) \frac{2}{3 x ^{\frac{1}{3}}})

Vereinfache

- 3 (- cot (x^{\frac{2}{3}}) csc (x^{\frac{2}{3}}) \frac{2}{3 x ^{\frac{1}{3}}}) : \frac{2 cot ( x ^{\frac{2}{3}} ) csc ( x ^{\frac{2}{3}} )}{x ^{\frac{1}{3}}}

= \frac{2 cot ( x ^{\frac{2}{3}} ) csc ( x ^{\frac{2}{3}} )}{x ^{\frac{1}{3}}}

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