derivative of-4tan(x-csc(x))

解

\frac{d}{d x} (- 4 tan (x) - csc (x))

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

解答ステップ

\frac{d}{d x} (- 4 tan (x) - csc (x))

和/差の法則を適用:

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

= - \frac{d}{d x} (4 tan (x)) - \frac{d}{d x} (csc (x))

\frac{d}{d x} (4 tan (x)) = 4 sec^{2} (x)

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

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

簡素化

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