derivative of (2x/(sqrt(sec(x))))

解

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

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

解答ステップ

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

定数を除去:

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

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

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 2 \cdot \frac{\frac{d x}{d x} sec ( x ) - \frac{d}{d x} ( sec ( x ) ) x}{( sec ( x ) ) ^{2}}

\frac{d x}{d x} = 1

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

= 2 \cdot \frac{1 \cdot sec ( x ) - \frac{t a n ( x ) s e c ( x )}{2} x}{( sec ( x ) ) ^{2}}

簡素化

2 \cdot \frac{1 \cdot sec ( x ) - \frac{t a n ( x ) s e c ( x )}{2} x}{( sec ( x ) ) ^{2}} : \frac{2 - x tan ( x )}{sec ( x )}

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