derivative-sec(1/x+7x)

解

導関数

- sec (\frac{1}{x} + 7 x)

- sec (\frac{1}{x} + 7 x) tan (\frac{1}{x} + 7 x) (- \frac{1}{x ^{2}} + 7)

解答ステップ

\frac{d}{d x} (- sec (\frac{1}{x} + 7 x))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (sec (\frac{1}{x} + 7 x))

連鎖法則を適用:

sec (\frac{1}{x} + 7 x) tan (\frac{1}{x} + 7 x) \frac{d}{d x} (\frac{1}{x} + 7 x)

= sec (\frac{1}{x} + 7 x) tan (\frac{1}{x} + 7 x) \frac{d}{d x} (\frac{1}{x} + 7 x)

\frac{d}{d x} (\frac{1}{x} + 7 x) = - \frac{1}{x ^{2}} + 7

= - sec (\frac{1}{x} + 7 x) tan (\frac{1}{x} + 7 x) (- \frac{1}{x ^{2}} + 7)