derivative-csc(x)-sin(x)

解

導関数

- csc (x) - sin (x)

cot^{2} (x) cos (x)

解答ステップ

\frac{d}{d x} (- csc (x) - sin (x))

和/差の法則を適用:

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

= - \frac{d}{d x} (csc (x)) - \frac{d}{d x} (sin (x))

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

\frac{d}{d x} (sin (x)) = cos (x)

= - (- cot (x) csc (x)) - cos (x)

簡素化

- (- cot (x) csc (x)) - cos (x) : cot^{2} (x) cos (x)

= cot^{2} (x) cos (x)