derivative of csc^2(2x-csc(2x^2))

解

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

- 4 csc^{2} (2 x) cot (2 x) + 4 x cot (2 x^{2}) csc (2 x^{2})

解答ステップ

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (csc^{2} (2 x)) = - 4 csc^{2} (2 x) cot (2 x)

\frac{d}{d x} (csc (2 x^{2})) = - cot (2 x^{2}) csc (2 x^{2}) \cdot 4 x

= - 4 csc^{2} (2 x) cot (2 x) - (- cot (2 x^{2}) csc (2 x^{2}) \cdot 4 x)

簡素化

= - 4 csc^{2} (2 x) cot (2 x) + 4 x cot (2 x^{2}) csc (2 x^{2})