derivative f(x)=-5cot(x)+3sec(x)

解

導関数

f (x) = - 5 cot (x) + 3 sec (x)

5 csc^{2} (x) + 3 sec (x) tan (x)

解答ステップ

\frac{d}{d x} (- 5 cot (x) + 3 sec (x))

和/差の法則を適用:

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

= - \frac{d}{d x} (5 cot (x)) + \frac{d}{d x} (3 sec (x))

\frac{d}{d x} (5 cot (x)) = - 5 csc^{2} (x)

\frac{d}{d x} (3 sec (x)) = 3 sec (x) tan (x)

= - (- 5 csc^{2} (x)) + 3 sec (x) tan (x)

簡素化

= 5 csc^{2} (x) + 3 sec (x) tan (x)