derivative y= 1/(cos(x/2))

解

導関数

y = \frac{1}{cos ( \frac{x}{2} )}

sec (\frac{x}{2}) tan (\frac{x}{2}) \frac{1}{2}

解答ステップ

\frac{d}{d x} (\frac{1}{cos ( \frac{x}{2} )})

簡素化

\frac{1}{cos ( \frac{x}{2} )} : sec (\frac{x}{2})

= \frac{d}{d x} (sec (\frac{x}{2}))

連鎖法則を適用:

sec (\frac{x}{2}) tan (\frac{x}{2}) \frac{d}{d x} (\frac{x}{2})

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

= sec (\frac{x}{2}) tan (\frac{x}{2}) \frac{1}{2}