derivative of csc(x^3+2x-tan(x))

解

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

- cot (x^{3} + 2 x) csc (x^{3} + 2 x) (3 x^{2} + 2) - sec^{2} (x)

解答ステップ

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

和/差の法則を適用:

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

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

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

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