derivative of csc^2(3x)

Lösung

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

- 6 csc^{2} (3 x) cot (3 x)

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= 2 csc (3 x) (- cot (3 x) csc (3 x) \cdot 3)

Vereinfache

2 csc (3 x) (- cot (3 x) csc (3 x) \cdot 3) : - 6 csc^{2} (3 x) cot (3 x)

= - 6 csc^{2} (3 x) cot (3 x)

\int cos (x) (3 + 4 sin^{2} (x)) d x

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