展開する (1-sec(x))(1+sec(x))'

解

展開する

(1 - sec (x)) (1 + sec (x))^{'}

(1 + sec (x))' - sec (x) (1 + sec (x))'

解答ステップ

(1 - sec (x)) (1 + sec (x))^{'}

分配法則を適用する:

a (b - c) = ab - a c

a = (1 + sec (x))^{'}, b = 1, c = sec (x)

= (1 + sec (x))^{^{'}} 1 - (1 + sec (x))^{^{'}} sec (x)

= 1 (1 + sec (x))^{^{'}} - sec (x) (1 + sec (x))^{^{'}}

乗算:

1 (1 + sec (x))^{'} = (1 + sec (x))^{'}

= (1 + sec (x))^{^{'}} - sec (x) (1 + sec (x))^{^{'}}